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Question 970958: A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr and the second half the speed was 40 km/hr. How far is the journey?

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13362)   (Show Source):
You can put this solution on YOUR website!

The other tutor provided a formal algebraic solution, using a standard method.

Here is a different, less formal solution.

Equal distances at different speeds in the ratio A:B means the times spent at the two speeds are in the ratio B:A.

In this problem, the two speeds are in the ratio 60:40 = 3:2, so the times spent at the two speeds are in the ratio 2:3.

The total time was 10 minutes; splitting that in the ratio 2:3 means the trip was 4 minutes (1/15 hour) at 60 km/h and 6 minutes (1/10 hour) at 40km/h.

Distance is rate times time, so the distance traveled at 60 km/h was km and the distance traveled at 40 km/h was km.

So the total distance was 4+4 = 8 km.

ANSWER: 8 km

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/hr
and the second half the speed was 40 km/hr. How far is the journey?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @lwsshak3 is incorrect, and his answer is absurdist.
        It is because his setup equation is wrong.

        I came to bring a correct solution.

let x = total distance of journey
x/2 = distance of first half of journey
x/2 = distance of second half of journey
travel time = distance/speed
10 min = 1/6 hr

Write the time equation

         + =

         + =

Multiply both sides by 120*80.

        80x + 120x = 1600
        200x = 1600
        x = 1600/20 = 8

How far is the journey?     8 km         <<<---=== ANSWER

CHECK for the total time      + = + = + = = of an hour.     ! precisely correct !

Solved correctly.

It confirms that @lwsshak3 regularly uses his computer code and practically never checks
and even never looks/reads what the code really produces.

Question 1149940: Craig is 4 years older than Colleen. Their total age is 76 years. How old are they? This is a linear equation.
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Craig is 4 years older than Colleen. Their total age is 76 years. How old are they? This is a linear equation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution and the answer in the post by @addingup are incorrect.
        Anyone can easy check incorrectness by adding the values of the @addingup answer.

        I came to bring a correct solution.

Let Colleen's age be x years.
Then Craig age is (x+4) years.         (Craig is 4 years older than Colleen)

x + (x+4) = 76         (their combined age)
2x + 4 = 76
2x = 76 - 4
2x = 72
x = 72/2
x = 36
So Colling is 36 years old and Craig is 36 + 4 = 40 years old.         ANSWER

Solved correctly.

Question 973912: A boy is 8 years old and his sister is twice his age if the boy turn 12 years old how old would his sister be
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!
Boy is 8, then his sister is 16. Age difference is 8 no matter when.
If the boy turned 12, then sister is still 8 years older. She then becomes 20.

Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

A boy is 8 years old and his sister is twice his age if the boy turn 12 years old how old would his sister be **************************************** @addingup(3677)'s answer, 24, is WRONG!! How RIDICULOUS is this answer? According to @addingup(3677)'s logic, boy is now twice his sister's age, and in 2 years' time. will also be twice her age. Never heard of such STUPID and NON-SENSICAL logic, if it could be called that! This is so SIMPLE, and is an ELEMENTARY-LEVEL easy-peasy problem....as easy as any problem could be!! How could someone get such a SIMPLE, 2nd grade math problem WRONG? Unbelievable!! Boy is 8, sister is twice his age, or 2(8) = 16 So, sister is 8 (16 - 8) years OLDER than the boy Therefore, when the boy is 12 (4 years from now), sister will be 4 years older too, or 16 + 4 = 20 SIMPLE, SIMPLE, SIMPLE. Doesn't even need algebra, just sheer common sense, and a little FOCUS!!!

Question 974858: If Joshua was a year older he would be three times as old as his brother. His brother is 4. How old is Joshua?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13362)   (Show Source):
You can put this solution on YOUR website!

Joshua's brother's age is 4, so three times his age is 12.

Joshua would be that age (12) if he were a year older, so Joshua is 11.

ANSWER: 11

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
If Joshua was a year older he would be three times as old as his brother. His brother is 4.
How old is Joshua?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @lwssthak3, giving the answer 14 years for Joshua's age is incorrect.
        The cause is that his setup equation is written incorrectly.
        Below see my correct solution.

let x=Joshua's age
x+1 = 3*4 = 12
x = 12 - 1 = 11
Joshua's age is 11 years.         ANSWER

Solved correctly.

Question 976631: 10 years ago man's age was6 times the sge of his son.12years later,the age of the son will be 27 years.what is the persent age of the father?
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
10 years ago man's age was 6 times the age of his son. 12 years later, the age of the son will be 27 years.
what is the present age of the father?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @lwsshak3, giving the answer 100 years for the father's age, is absurdist and incorrect.
        The cause of the mistake is that @lwsshak3 lost the logic line on his way.

        I came to bring a correct solution.

        The problem itself is extremely simple and can be solved mentally, without using equations.

        When I was in front of dilemma "what to provide - a routine algebra solution
        or a shining mental solution" - I could not resist and chose a shining mental solution.

The problem says "12 years later, the age of the son will be 27 years." This means that the current age of the son is 27-12 = 15 years. Hence, 10 years ago the son was 15-10 = 5 years old. At that time, the father's age was 6 times the sun's age, i.e. 6*5 = 30 years. Hence, the present age of the father is 30 + 10 = 40 years. ANSWER. The present age of the father is 40 years.

Solved correctly in the form accessible for a 4-th grade student
to teach him to build a logic line and to keep it firmly.

It is the way, how a responsible teacher should teach,
if he wants the seeds he sowed produce right shoots.

/////////////////////////////////

I said earlier in one of my posts that the method which @lwsshak3 regularly uses is a computer code.
This problem, solved incorrectly by @lwsshak3, remarkably confirms this my hypothesis/observation.
@lwsshak3 made a rude OBVIOUS error, but yet he did not even waver, showing total absence of a normal human reaction.

It is why such "teachers"/"tutors" are dangerous participants of an education process -
because they have no built-in function of self-checking,
as well as they have no feeling of responsibility for their production.
Their only goal is to occupy as much territory as possible.

It is just as if sappers were laying mines in the path of their own army's advance.

Question 862659: Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old
as Grandma was when Grandpa was as old as Grandma is now.
~~~~~~~~~~~~~~~~~~~~~~~

Let P be the grandpa age (in years), and let M be the grandpa age. First equation is P + M = 140. (1) When Grandpa was as old as Grandma ? - It happened (P-M) years ago. At that time, Grandma was M - (P-M) = 2M - P years old, while Grandpa was P - (P-M) = M years old. So, our second equation is M = 2(2M-P), or M = 4M - 2P, which we transform to 2P = 3M. (2). So, we transform first equation (1) to 2P + 2M = 280, and then replace there 2P by 3M, based on (2). We get then 3M + 2M = 280, 5M = 280, M = 280/5 = 56. At this point the solution is complete. ANSWER. Currently, grandma is 56 years old.

Solved.

Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now. ********************************************** Let Grandpa's and Grandma's ages, be P, and M, respectively SInce their ages sum to 140, we get: P + M = 140___M = 140 - P ---- eq (i) "Grandpa was as old as Grandma is now," clearly signifies that Grandpa is older than Grandma, which means that the difference in their ages is: P - M When was Grandpa as old as Grandma is now? This is the SAME as the difference in their ages, or P - M = P - (140 - P) = P - 140 + P = "2P - 140" years ago So, when Grandpa was as old as Grandma is now, Grandpa was: M, or "140 - P" years-old And, when Grandpa was as old as Grandma is now, Grandma was: 140 - P - (2P - 140) = 140 - P - 2P + 140 = - 3P + 280 Finally, since "Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now," we have: 140 - P = 2(- 3P + 280) 140 - P = - 6p + 560 - P + 6P = 560 - 140 5P = 420 Grandpa's age, or Therefore, Grandma is 140 - P = 140 - 84 = 56

Question 985149: The average age of Alice and tom is 14 years 3 months. Alice is 2 years 8 months younger than tom. How old is Alice ?
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
The average age of Alice and tom is 14 years 3 months.
Alice is 2 years 8 months younger than tom.
How old is Alice ?
~~~~~~~~~~~~~~~~~~~~~~~~~~

        As I read the solution in the post by @lwsshak3,
        I nearly died of horror — so many crude errors/mistakes are there.

        For correct solution, see what follows in my post.

Let x be the Alice age in months, and let y be the Tom age in months. 14 years and 3 months is 14*12+3 = 171 months. Therefore, the first statement means that the sum x and y is 2*171 = 342 months. So, our first equation is y + x = 342 months. (1) 2 years and 8 months is 2*12+8 = 32 months. Therefore, the second statement means that the difference y - x is 32 months. So, our second equation is y - x = 32 months. (2) From equations (1) and (2), - the greatest age (which is the Tom age) is half of the sum 342 and 32, i.e. = 187 months, - while the smallest age (which is the Alice age) is half of the difference of numbers 342 and 32, i.e. = 155 months. ANSWER. Alice is 155 months old.

Solved correctly for your secure teaching/learning.

Ignore the post by @lwsshar3, since it is full of errors.

Question 879932: my mum was 27 years old when she gave birth to me 8 years ago she was twice as
old has i would be in 5 years how old am i
Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

my mum was 27 years old when she gave birth to me 8 years ago she was twice as old has i would be in 5 years how old am i ****************************************** A WRONG answer, AGAIN, just like the "respondent" who replied to "Age_Word_Problems/510453" AGAIN, I am NOT 22, as the other person states. My ACTUAL/CORRECT age is 9. While this may seen trivial, this AUTHOR wonders why this "respondent," as well as the one who answered "Age_Word_Problems/510453," deem the narrator to be the mum's son!!

Question 510453: This is an age old problwm.
My mum was 27 when i was born. 8 Years ago she was twice as old as i shall be in 5 years, time. How old am i now
Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

This is an age old problwm. My mum was 27 when i was born. 8 Years ago she was twice as old as i shall be in 5 years, time. How old am i now ***************** I am NOT 25, as the other person states. Let my age, be M Then my mum is M + 27, since she was 27 when I was born 8 years ago, my mum was M + 27 - 8 = M + 19 In 5 years, I'll be M + 5 "8 Years ago she was twice as old as i shall be in 5 years, time," translates to: M + 19 = 2(M + 5) M + 19 = 2M + 10 M - 2M = 10 - 19 - M = - 9 My age, or

Question 952520: 20 years ago Grandma was twice as old as Mum. Today, Grandma is twice the age Mum was when I was born. How old am I?
Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

20 years ago Grandma was twice as old as Mum. Today, Grandma is twice the age Mum was when I was born. How old am I? ************************************** Let Grandma's current age, be G, and Mum's, M Then 20 years ago Grandma was G - 20, and Mum was M - 20 Given that, "20 years ago Grandma was twice as old as Mum," gives us: G - 20 = 2(M - 20) ===> G - 20 = 2M - 40 ===> G = 2M - 40 + 20 ===> G = 2M - 20 ---- eq (i) G - 20 = 2(M - 20) ===> G - 20 = 2M - 40____G - 20 + 40 = 2M ===> G + 20 = 2M ====> ----- eq (ii) Let the number of years since my birth, be y Mum's age, when I ws born: M - y, or "Today, Grandma is twice the age Mum was when I was born," gives us: G = 2(M - y) ----- Substituting for M G = G + 20 - 2y G - G - 20 = - 2y ---- Subtracting 20 from each side - 20 = - 2y Years since I was born/my age, or

Question 492671: Hi there, I have to figure out how old the youngest person will be when I am three times his age. I have done the problem and I keep getting an answer that states how old we were 8 years ago. Currently I am 32 and the youngest person is 16. Please help! I think I am doing it correctly but I just want to make sure I am.
Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

Hi there, I have to figure out how old the youngest person will be when I am three times his age. I have done the problem and I keep getting an answer that states how old we were 8 years ago. Currently I am 32 and the youngest person is 16. Please help! I think I am doing it correctly but I just want to make sure I am. ***** Your are correct, as stated by the other person who responded. Let the number of years when you will be 3 times the youngest person's age, be y Since you're now 32, at that time, you will be 32 + y And, since the youngest person is now 16, at that time, he/she will be 16 + y As you will be 3 times the youngest person's age, then, we get the following equation for the number of years when that will be, as: 32 + y = 3(16 + y) 32 + y = 48 + 3y y - 3y = 48 - 32 - 2y = 16 Number of years when you'll be THRICE the youngest person's age, or If you did it this way, you may've been confused by the answer, but it's quite correct. The value of y, - 8, actually indicates that the time when you'll be 3 times the youngest person's age, is - 8, or 8 YEARS AGO. So, 8 years ago, you were 32 - 8 = 24, and the youngest person was: 16 - 8 = 8. You were 24 when he/she was 8, which made you 3 times his/her age, 8 years ago (or - 8)

Question 283256: A mother is twice as old as her daughter now, but 10 years ago, she was 3 times as
old as her daughter. Find their ages at present.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
A mother is twice as old as her daughter now, but 10 years ago, she was 3 times as
old as her daughter. Find their ages at present.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        In the post by @mananth, the setup equation is written incorrectly.
        His manipulations that follow this incorrect equation, also have many errors,
        although the final answer is correct.

        His solution can not be considered as an etalon, so I came to bring a correct solution.

Let the daughter's age be x
mother's age will be 2x
Ten years ago
daughter's age x-10
Mother's age 2x-10

3(x-10) = 2x-10         <<<---=== This is a CORRECT setup equation

Simplify and find 'x'

3x-30 = 2x-10
3x-2x = 30-10
x = 20 Daughter's age now
Mother's age is 2x = 2*20 = 40 years

Solved correctly.

Question 1002578: Question: Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad, and in 7 years his grandpa will be four times older than Jake. How old is Jake's dad?
I've tried 13*4=52. 52-7=45. 45+3=48. 48/2=24.
I'm not sure what steps I'm missing or what math I'm doing wrong
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad,
and in 7 years his grandpa will be four times older than Jake. How old is Jake's dad?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        As printed in the post, this problem is a lame horse with three legs.
        Why ? - Because no one professional English writer will write "will be four times older than Jake".
        Why ? - Because it is not accepted in English to formulate Math problems using this form.

        So, I will interpret the whole problem in THIS way

Jake is 13 years old. In 3 years his grandpa will be twice as old as Jake's dad, and in 7 years his grandpa will be four times as old as Jake. How old is Jake's dad?

        In this form, the problem is a nice arithmetic problem to solve it MENTALLY by reasoning.

Jack is 13 years old now. In 7 years, Jack will be 13+7 = 20 years old. Hence, in 7 years, Jack's grandpa will be 20*4 = 80 years old. It means that Jack's grandpa is 80-7 = 73 years old now. In 3 years, the grandpa will be 73+3 = 76 years old. Hence, in 3 years, Jack's father will be 76/2 = 38 years old. It means that Jack's father is 38-3 = 35 years old now. ANSWER

Solved in this interpretation.

This problem is a good exercise, since it teaches a student to build a logical chain of steps.

Question 973010: Hi,
I have been trying to solve a word problem, here it is:
Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?

I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation
Thanks
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!

3 years ago today 1 year future Evan y-3 y y+1 Sister 3(y-3)=x-3 x 2(y+1)=x+1

from first equation

from second equation

Subtracting,
, Evan's age today

, his sister's age today

Answer by MathTherapy(10849)   (Show Source):
You can put this solution on YOUR website!

Hi, I have been trying to solve a word problem, here it is: Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now? I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation Thanks ****************************** Let Evan's age be E, and his sister's, S "Three years ago, Evan was one third of his sister's age....." translates to: ------ eq (i) "In a year's time, Evan's age doubled will match his sister's age.....translates to: 2(E + 1) = S + 1 2E + 2 = S + 1 2E + 2 - 1 = S 2E + 1 = S ------ eq (ii) ---- Substituting 2E + 1 for S, in eq (i) 3E - 9 = 2E - 2 ----- Multiplying by LCD, 3 3E - 2E = - 2 + 9 Evan's age, or E = 7

Question 1031850: A man is 4 times old as his daughter was 3 years ago.If their combined ages is 48,how old is the daughter now?

Found 3 solutions by josgarithmetic, n2, ikleyn:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!

Three years ago Now MAN - 4(d-3) DAUGHTER d-3 d SUM 48

, daughter's age

Answer by n2(91)   (Show Source):
You can put this solution on YOUR website!
.
A man is 4 times old as his daughter was 3 years ago.
If their combined ages is 48,how old is the daughter now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the daughter age be x now. 3 years ago her age was (x-3) years. Father's age now is 4(x-3) Our equation is x + 4(x-3) = 48 (the combined age) Simplify and find x x + 4x - 12 = 48 5x = 60 x = 60/5 = 12. ANSWER. The daughter is 12 years old. The father is 4(x-3) = 4*(12-3) = 4*9 = 36 years old. CNECK. Their combined age is 12 + 36 = 48, which is precisely correct.

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
A man is 4 times old as his daughter was 3 years ago.
If their combined ages is 48,how old is the daughter now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is incorrect.
        It is incorrect, since his setup equation is wrong.

        I came to bring a correct solution.

Let the daughter age be x now. 3 years ago her age was (x-3) years. Father's age now is 4(x-3) Our equation is x + 4(x-3) = 48 (the combined age) Simplify and find x x + 4x - 12 = 48 5x = 60 x = 60/5 = 12. ANSWER. The daughter is 12 years old. The father is 4(x-3) = 4*(12-3) = 4*9 = 36 years old. CNECK. Their combined age is 12 + 36 = 48, which is precisely correct.

Solved correctly.

Question 1137386: If Amber's age is fourteen less than three times her age six years ago, she will be sixteen years older than her current age. How old is Amber?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!
Current age, n
Age at six years ago, n-6

This part on its own: Amber's age is fourteen less than three times her age six years ago
That would be
and the description an question which came after are nonsense.

Just solving the formed equation

Amber is 16 years old.

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
If Amber's age is fourteen less than three times her age six years ago,
she will be sixteen years older than her current age. How old is Amber?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        How the problem is formulated/worded/presented in the post, is a blatant nonsense,
        contradicting to human logic.

        The solution by @mananth makes this nonsense in degree 2.

        The solution by Artificial Intelligence (Google overview of Feb.09, 2026) repeats this nonsense.

https://www.google.com/search?q=If+Amber%27s+age+is+fourteen+less+than+three+times+her+age+six+years+ago%2C+she+will+be+sixteen+years+older+than+her+current+age.+How+old+is+Amber%3F&rlz=1C1CHBF_enUS1071US1071&oq=If+Amber%27s+age+is+fourteen+less+than+three+times+her+age+six+years+ago%2C+she+will+be+sixteen+years+older+than+her+current+age.+How+old+is+Amber%3F&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIHCAEQIRiPAjIHCAIQIRiPAtIBCDEwMTNqMGo3qAIIsAIB8QX2P9qU19kUUvEF9j_alNfZFFI&sourceid=chrome&ie=UTF-8

        One condition is just enough to solve the problem completely, and the second condition
        is illogical and is not consistent with the first condition.

        So, the reasonable modification to the problem is THIS:

                If Amber's age is fourteen less than three times her age six years ago, how old is Amber?

        Below is my solution for this modified version.

Let 'x' be the Amber's age now. Then the problem leads to this equation 3*(x-6) - 14 = x. Simplify and find x 3x - 18 - 14 = x, 3x - 32 = x, 3x - x = 32, 2x = 32, x = 32/2 = 16. ANSWER. Amber is 16 years old now.

Solved.

-----------------------

Again, the original formulation of the problem is nonsense.

The solution by @mananth is nonsense in degree 2.

The referred solution by the AI is nonsense, too, repeating the nonsense by @mananth.

A reasonable modification and a solution are presented in my post above.

Always remember that @mananth is not a person. It is a computer code,
which may work correctly or incorrectly, but, in distinction of a normal human,
this code does not know in which mode he currently works - in the right mode or in the wrong mode.
This understanding is outside of the range of its abilities.

            I N T E R E S T I N G

Today, on Feb.09, 2026, I posted this original formulation to other AI site, math-chat.org.

It was smart enough to recognize that the original formulation is/was defective,
and was smart enough to create a reasonable version, exactly as mine.
It also solved completely for this modified formulation, so it acted as a reasonable human and a qualified solver.

Thus I conclude that AI Google Overview is just outdated version of AI.
Why then they keep its outcome in the first position of the Google search output? - It is just out of logic.

All this information was posted to the Google Overview via their feedback system
with the reference to this web-page.

Question 1154747: When Mrs. Lee poured the soup into a pan it was room temperature. if the room was 85*F and the soupès temperature went up by 15.5*F per minute, about how long would it take for the soup to boil
Answer by ikleyn(53908)   (Show Source):
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.
When Mrs. Lee poured the soup into a pan it was room temperature. if the room was 85*F and
the soupès temperature went up by 15.5*F per minute, about how long would it take for the soup to boil
~~~~~~~~~~~~~~~~~~~~~~

In his post, @mananth made a fatal error.

He missed to convert boiling point 100 deg Celsius to degrees Fahrenheit, 212 F,
and got absurdist answer.

So, we should calculate the time as

        t = = 8.194 minutes, or about 8 minutes and 12 seconds.

Solved correctly.

Question 1203623: jack is 7 years older than mia. the sum of there ages is 53.how old is jack.

Answer by ikleyn(53908)   (Show Source):
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.
Jack is 7 years older than Mia. The sum of their ages is 53. How old is Jack.
~~~~~~~~~~~~~~~~~~~~~~~

Again, it is nice problem to solve it MENTALLY in 6 seconds, without using equations.

Indeed, consider/imagine another person Jack' instead of Jack, who (Jack') is 7 years younger than Jack.

Then Jack' and Mia both are of the same age, and the sum of their ages is 53-7 = 46.

Hence, Jack' is 46/2 = 23 years old.

It implies that Jack, the true person, is 23 + 7 = 30 years old.

At this point, the solution is complete.

Question 1204081: the combined age of 2 brothers is 35 years old.7 years ago one brother was twice the age of the other. how many years apart were they born

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
the combined age of 2 brothers is 35 years old. 7 years ago one brother was twice the age of the other.
how many years apart were they born
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        Nice/ideal problem to solve it MENTALLY, without using equations.

Seven years ago the combined age of the two brothers was 35 - 7 - 7 = 21 years. In addition, we are given that 7 years ago (i.e., at that time), one brother was twice the age of the other. It means (as anyone can get immediately), that 7 years ago the older brother was 14 years old, while the younger brother was 7 years old at that time. Hence, the brothers were born 14-7 = 7 years apart.

Solved.

As clear as 2 - 1 = 1.

Compare with the solution by @mananth.

Question 437671: Cory's age is 20% of her father's age. Forty-two years from now, Cory's age will be two-thirds (2/3) of her father's age. How old are Cory and her father now?
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.

In his post, @manath correctly determined the Cory's age: it is 6 years.

But the age of the father is determined incorrectly by @manath.

The correct answer is: the father is 6*5 = 30 years old.

Question 434074: The sum of the present ages of john and his father is 89 years. After 11 years the age of father will be twice the age of john at that time, find their present ages.
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13362)   (Show Source):
You can put this solution on YOUR website!

Given that John's father will be twice as old as John is 11 years from now....

let x = John's age 11 years from now
then 2x = father's age 11 years from now
then x-11 = John's age now
and 2x-11 = father's age now

The sum of their present ages is 89:

(x-11)+(2x-11) = 89
3x-22 = 89
3x = 111
x = 37

John's present age = x-11 = 37-11 = 26
father's present age = 2x-11 = 74-11 = 63

ANSWERS: 26 and 63

---------------------------------------------------------------

I chose to set the problem up in a different way than the other tutors.

Sometimes that can make a big difference in how much work it takes to solve the problem.

It didn't make much difference in this problem....

Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!

NOW IN 11 YEARS John 89-m 89-m+11=100-m Father m m+11 SUM 89 89+2*11=111

Description makes that .

John's Father, 63
John, 26

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
The sum of the present ages of john and his father is 89 years.
After 11 years the age of father will be twice the age of john at that time,
find their present ages.
~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is incorrect.
        His setup and his treatment of equations is erroneous and leads right to abyss.
        I came to make a job accurately and to teach you properly.

john's age =x
father's age = 89-x
..
after 11 years
john's age = x+11
father's age = (89-x)+11 = 100 - x
...
100 - x = 2(x+11)
100 - x = 2x + 22
100 - 22 = 2x + x
78 = 3x
x = 78/3 = 26.

ANSWER. John is 26 years old. The father is 89-26 = 63 years old.

Solved correctly.

Question 426356: A father is nine times the age of his son. In 5 years he will be four times the age of his son. How old are they now?
Found 2 solutions by timofer, ikleyn:
Answer by timofer(159)   (Show Source):
You can put this solution on YOUR website!

NOW IN 5 YEARS Father 9x 9x+5 Son x x+5

the son now
Father now,

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
A father is nine times the age of his son. In 5 years he will be four times the age of his son.
How old are they now?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The answer in the post by @mananth is incorrect.
        I came to bring a correct solution (including the answer).

Son's age x Father's age 9x 5 years later Son's age x +5 Father's age 9x+5 In 5 years, the father's age is four times the son age 9x + 5 = 4(x+5) 9x + 5 = 4x + 20 5x = 20-5 5x = 15 /5 x = 3 years Son's age 9x = 27 years Father's age

Solved correctly.

Question 732523: Sally is 10 years older than Tim. In 8 years, the sum of their ages will be 40. Determine how old Sally and Tim are now.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!
x Sally
y Tim

and .

.
.
.

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Sally is 10 years older than Tim. In 8 years, the sum of their ages will be 40.
Determine how old Sally and Tim are now.
~~~~~~~~~~~~~~~~~~~~~~~~

        The solution to this problem in the post by @lynnlo is incorrect.
        I came to bring a correct solution.

Let x be the Tim's age. Then the Sally's age is (x+10) years. In 8 years, Tim's age is (x+8) years, while Sally's age is ((x+10)+8) = (x+18) years. In 8 years, the sum of their ages will be 40 - so we write this equation (x+8) + (x+18) = 40. Simplify and find 'x' 2x + 26 = 40, 2x = 40 - 26 = 14, x = 14/2 = 7. Thus Tim is 7 years old now; Sally is 7+10 = 17 years old now. <<<---=== ANSWER CHECK. (7+8) + (17+8) = 15 + 25 = 40. ! correct !

Solved correctly.

Question 733057: you deposited $45.25 in your checking account. but instead of adding $45.25 to your balace the bank accidentally substracted $45.25. How much money should the bank add to your account to correct the mistake?
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.

The bank should add twice as $45.25, i.e. $90.50 to your account to correct the mistake.

As to me, it should be clear even for a hedgehog.

Question 733673: steven is 6 years older than his sister claudia. The product of the ages of both siblings is 187.Find an equation and calculate the age of steven and claudia
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
steven is 6 years older than his sister claudia. The product of the ages of both siblings
is 187.Find an equation and calculate the age of steven and Claudia
~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the sister's age. Then Steven is (x+6) years old. Write the product equation x*(x+6) = 187. You can reduce it to quadratic equation and solve it via the quadratic formula. But more intelligent way is to notice that in the number 187 the alternate sum of its digits, 1 - 8 + 7 = 0; hence, 187 is divisible by 11. It gives us 11 year for the age of the sister and 11+6 = 17 years for Steven. ANSWER. Claudia is 11 years old. Steven is 17 years old.

Solved.

The solution by @lynnlo is incorrect.

Question 744574: the present age of a father is equal to the sum of ages of his 5 children. 12 years hence the sum of ages of his children will be twice the age of their father. find the present age of the father.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website!
FIVE children, one father
y, age of father
C, sum of ages of the five children

---------the description

Using second equation

substituting for C,

father's current age

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
the present age of a father is equal to the sum of ages of his 5 children.
12 years hence the sum of ages of his children will be twice the age of their father.
find the present age of the father.
~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the present age of the father. According to the problem, x is equal to the sum of the 5 his children, at the same time. 12 years later, the sum of ages of 5 children will be x+5*12 = x+60 years. At that time the age of the father will be x+12 years. The problem says that 2(x+12) = x + 5*12. To find x, simplify this equation step by step 2x + 24 = x + 60 2x - x = 60 - 24 x = 36. ANSWER. The father is 36 years old now.

Solved.

Question 744595: if father tell his son,i was of your present age where you were born.if the father is 36 now . how old the boy 5 year back.
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
if father tell his son, I was of your present age where you were born.
if the father is 36 now . how old the boy 5 year back.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

if father tell his son, "I was of your present age where you were born", it means that the father age now is twice the son present age. So, if the father is 36 years old now, then his son is 36/2 = 18 years old. Hence, 5 years back the son was 18-5 = 13 years old. ANSWER

Solved.

Question 794514: Mrs. Lemecha's dad is 5 times as old as he was 40 years ago? how old is Mrs. Lemecha's dad?
Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Mrs. Lemecha's dad is 5 times as old as he was 40 years ago? how old is Mrs. Lemecha's dad?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

        This is a nice problem, but the solution given in the post by @lynnlo is absolutely incorrect.
        I came to bring a correct solution.

Let x be the age of the dad. 40 years ago his age was (x-40) years. Write equation as you read the problem x = 5(x-40) Simplify it step by step and find x x = 5x - 5*40, x = 5x - 200 Collect the terms with 'x' on the right side; move the constant term -200 to the left side changing its sign 200 = 5x - x 200 = 4x x = 200/4 = 50. ANSWER. The dad is 50 years old.

Solved.

This problem teaches to read problem attentively and to make setup accurately and adequately.

Therefore, this problem has great educational/instructional value and teaches to treat Math problems with respect.

Question 674243: Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor, five years after he was married, he had a son who died 4 years before his father at half his father's final age. How long did bob live?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13362)   (Show Source):
You can put this solution on YOUR website!

Solving the problem using all of the given information is a good exercise. However, logical reasoning gives the answer with very little work.

In age problems, all numbers are whole numbers. So in this problem, the age Bob lived to must be a multiple of 6, 12, and 7.

The least common multiple of 6, 12, and 7 is 84; so the age Bob lived to is an integer multiple of 84. Since twice 84 is an unreasonable answer for the age at which Bob died, the answer has to be 84.

ANSWER: 84

Answer by ikleyn(53908)   (Show Source):
You can put this solution on YOUR website!
.
Bob spent 1/6 of his life as a child, 1/12 as an adolescent, and 1/7 as a bachelor,
five years after he was married, he had a son who died 4 years before his father
at half his father's final age. How long did bob live?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Wording in your post is not perfect, but don't despair. There is a classic
well known story problem about Diophantus, famous mathematician of ancient Greece.

Diophantus's youth lasts 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly half as long as his father, and Diophantus died just four years after his son's death. What was his age when he died?

This story problem is precisely what you want to follow literally. So, I will solve it for you.
Again, it is classic of about 2200 years old.

Let x be the Diophantus' age when he died. As we read the problem, we write this equation x = + + + 5 + + 4. To solve, multiply all the terms by the Greatest Common Denominator, which is 12*7 = 84. You will get 84x = 14x + 7x + 12x + 5*84 + 42x + 4*84. Group like terms in right side 84x = (14 + 7 + 12 + 42)x + (5*84 + 4*84), combine like terms 84x = 75x + 756, simplify and find x 84x - 75x = 756, 9x = 756, x = 756/9 = 84. Thus, Diophantus died at the age of 84 years.

Solved.

About Diophantus, read this remarkable Wikipedia article

https://en.wikipedia.org/wiki/Diophantus

https://en.wikipedia.org/wiki/Diophantus

Enjoy ( ! )

Question 626199: my daughter is in year 6 at school and has been given maths homework which i cant help her with i have 2 questions but need to be able to show workings out and be able to understand how we got the answer.
1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit. the sum of the three digits is 4. what number is fatma thinking off
2)who am i, i have 3 digit i can only be divived by myself and one. the sum of my digits is 11 i am under 150
Answer by n3(7)   (Show Source):
You can put this solution on YOUR website!
.
1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit.
the sum of the three digits is 4. what number is fatma thinking off
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since the 3-digit number is odd, its last (the ones) digit is 1, or 3, or 5, or 7, or 9. If the last digit is '1', then the hundreds digit is 3 and their sum is just 1 + 3 = 4. So (a) then the tens digit is 0 and (b) the number itself is 301. In addition, it is clear that the restriction " the sum of digits is 4 " makes other options for the last digit IMPOSSIBLE. So, the answer to this problem is .

Solved.