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Find the rates of walking and cycling.
1 solutions
Answer 429828 by ankor@dixie-net.com(15746)   on 2012-12-29 15:50:04 (Show Source):
You can put this solution on YOUR website!If Mr. Norton walks for 2 miles and then cycles for 6 miles, it takes him 1 hr and 24 min to go the total distance of 8 miles
....but if he walks for 5 miles and cycles for 3 miles the rates of walking and cycling being the same as before, the total time taken is 2 hr and 18 min.
Find the rates of walking and cycling.
:
let w = his walking speed
let c = cycling speed
:
change 1 hr 24 min to: 1 + 24/60 = 1.4 hrs
change 2 hr 18 min to: 2 + 18/60 + 2.3 hrs
:
Write time equation for scenario
 +  = 1.4
and
 +  = 2.3
:
multiply the above equation by 2wc and mult the 1st equation by wc
10c + 6w = 4.6wc
2c + 6w = 1.4wc
--------------------subtraction eliminates w, find c
8c = 3.2wc
divide both sides by c
8 = 3.2w
w = 8/3.2
w = 2.5 mph walking speed
:
Find the cycling speed using eq: + = 1.4
 + = 1.4
.8 + = 1.4
= 1.4 - .8
= .6
c = 6/.6
c = 10 mph is the cycling speed
:
:
Check this in the equation: + = 2.3
 +  =
2 + .3 = 2.3
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percentage/697240: There are twice as many boys as girls in the class. if 20% of the boys and 35% of the girls have already handed over their result cards, what percent of the students have not yet handed over their result cards?
1 solutions
Answer 429809 by ankor@dixie-net.com(15746) on 2012-12-29 13:20:44 (Show Source):
You can put this solution on YOUR website!There are twice as many boys as girls in the class.
let x = no. of girls
then
2x = no. of boys
and
3x = total number of students
:
if 20% of the boys and 35% of the girls have already handed over their result cards, what percent of the students have not yet handed over their result cards?
:
 =  = 
Cancel x
 * 100 = 25% of the students have handed theirs in, therefore
75% have not.
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Volume/697106: John made a cubical lantern. The total length of its edges is 36 dm. What is the total surface area that he has to cover?
1 solutions
Answer 429674 by ankor@dixie-net.com(15746) on 2012-12-28 09:23:56 (Show Source):
You can put this solution on YOUR website!John made a cubical lantern.
The total length of its edges is 36 dm.
What is the total surface area that he has to cover?
:
A cube has 12 edges, therefore one edge: 36/12 = 3 dm
:
A cube has 6 sides, therefore:
Surface area of a cubes 6 time the area of each side
S.A. = 6 * 3^2
S.A. = 54 sq/dm
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Equations/697090: solve the following algebraically:
I see that both sides of the equation have a  the only exception is the +4. I'm not sure what I am supposed to do with the four. Should I put a one under it? I don't understand how I am supposed to solve for "x"
1 solutions
Answer 429649 by ankor@dixie-net.com(15746) on 2012-12-27 22:02:38 (Show Source):
You can put this solution on YOUR website!solve the following algebraically:
Actually there is no solution, but plunging ahead anyway
:
multiply thru by (x-3) and you have
2 + 4(x-3) = 2
Subtract 2 from both side
4(x - 3) = 0
4x - 12 = 0
4x = 12
x = 12/4
x = 3
:
Now you can see if you replace x with 3, in the original equation we have division by 0, hence no solution
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Age_Word_Problems/697072: I know a priest who is 44 years old. Sometime ago, he was twice as old as I. In the following year he was one and a half times older than I.
How old am I now?
1 solutions
Answer 429648 by ankor@dixie-net.com(15746) on 2012-12-27 21:55:58 (Show Source):
You can put this solution on YOUR website!I know a priest who is 44 years old.
Sometime ago, he was twice as old as I.
In the following year he was one and a half times older than I.
How old am I now?
:
We can approach this with this relationship:
let p = priest's age some time ago
let a = your age some time ago
Find the age in which p is twice a, and one year later p is 1.5a
:
2a = p
and one year later
1.5(a+1) = p + 1
1.5a + 1.5 = p + 1
1.5a = p + 1 - 1.5
1.5a = p - .5
replace p with 2a
1.5a = 2a - .5
1.5a - 2a = -.5
-.5a = -.5
a = 1 year old some time ago
and
p = 2 yrs old some time ago
then one year later:
a = 2, then p = 3, we know that 1.5(2) = 3
there is only one year difference, therefore when the priest is 44 you are 43
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Travel_Word_Problems/697055: Two cars leave a gas station and head in the same direction. Car A travels at 35 mph, while car B travels at 45 mph. If Car B leaves two hours after Car A, how many miles from the gas station will Car B catch up to Car A?
1 solutions
Answer 429632 by ankor@dixie-net.com(15746) on 2012-12-27 19:52:43 (Show Source):
You can put this solution on YOUR website!Two cars leave a gas station and head in the same direction.
Car A travels at 35 mph, while car B travels at 45 mph.
If Car B leaves two hours after Car A,
how many miles from the gas station will Car B catch up to Car A?
:
Find the time required for car B to catch car A
:
Let t = travel time of Car B
then
(t+2) = travel time of Car A
:
When B catches A, they will have traveled the same distance.
Write a distance equation: Dist = speed * time
:
45t = 35(t+2)
45t = 35t + 70
45t - 35t = 70
10t = 70
t = 70/10
t = 7 hrs is the travel time of car B
then
7 + 2 = 9 hrs is the time of Car A
:
"how many miles from the gas station will Car B catch up to Car A?"
7 * 45 = 315 mi from the station
confirm this with Car A
9 * 35 = 315 mi
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�t�e�s�t/697035: Find the x and y intercept of the line through point P(-3,2) which is parallel to the line 4x-5y = 17
can you please help me? Thanks so much in advance.
1 solutions
Answer 429617 by ankor@dixie-net.com(15746) on 2012-12-27 16:32:03 (Show Source):
You can put this solution on YOUR website! Find the x and y intercept of the line through point P(-3,2) which is parallel to the line 4x-5y = 17
:
Parallel lines have the same slope, put the equation in the slope/intercept form
4x - 5y = 17
subtract 4x from both sides
-5x = -4x + 17
y has to be positive, multiply both sides by -1
5y = 4x - 17
y has to have a coefficient of 1, divide both sides by 5
y =  x - 
:
Now we know the slope = 4/5
:
Use the point slope equation to find the equation of the parallel line
y - y1 = m(x - x1), where:
x1 = -3, y1 = 2, m = 4/5
y - 2 = (x -(-3))
y - 2 = x + 
y - 2 = x + 2.4
y = x + 2.4 + 2
y = x + 4.4, is the equation of the parallel line passing thru -3,2
:
Confirm this, replace x with -3 and solve for y, should = 2
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Graphs/697025: what is the slope of 2x+y=2.
i dont know if i should subtract the two. or get rid of the two next to the x or just leave the x as 0. please help.
1 solutions
Answer 429595 by ankor@dixie-net.com(15746) on 2012-12-27 13:36:14 (Show Source):
You can put this solution on YOUR website!what is the slope of 2x+y=2.
:
You want to put the equation into the slope/intercept form which is y = mx + b
:
2x + y = 2
subtract 2x from both sides
y = -2x + 2
This is the slope/intercept form, the slope (m) is -2
|
Money_Word_Problems/696942: Bob is buying buildings. The cost of each building increases by 10% of the cost of the first building. If the cost of the first building is 2.7million, how much would number 10,000 cost
1 solutions
Answer 429567 by ankor@dixie-net.com(15746) on 2012-12-27 08:46:53 (Show Source):
You can put this solution on YOUR website!Bob is buying buildings.
The cost of each building increases by 10% of the cost of the first building.
If the cost of the first building is 2.7million, how much would number 10,000 cost?
:
Let A = cost of 10000th building in millions
A = 2.7 + (.1*10000*2.7)
A = 2.7 + 2700
A = 2702.7 million
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Rate-of-work-word-problems/696715: 2 pipes fill a tank in 10 minutes, large pipe fill twice the smaller and out of one pipe empty 45 minutes. how much time taken by the small pipe to fill
1 solutions
Answer 429543 by ankor@dixie-net.com(15746) on 2012-12-26 21:01:50 (Show Source):
You can put this solution on YOUR website!2 pipes fill a tank in 10 minutes, large pipe fill twice the smaller and out of one pipe empty 45 minutes.
how much time taken by the small pipe to fill?
:
Let t = time for the small pipe to fill the tank (in minutes
then
.5t = time for the large pipe to fill it
:
let the completed job = 1 (a full tank
:
 +  = 1
multiply by t
2(10) + 10 = t
20 + 10 = t
t = 30 min for the small pipe working alone
|
Numbers_Word_Problems/696881: A number consists of two digits. The sum of the digit is 10. On reversing the digits of the number, the number decreases by 36. What is the product of the two digits ?
1 solutions
Answer 429437 by ankor@dixie-net.com(15746) on 2012-12-26 09:42:52 (Show Source):
You can put this solution on YOUR website!A number consists of two digits.
let a = the tens digit
let b = the units
then
10a+b = the "number"
:
The sum of the digit is 10.
a + b = 10
:
On reversing the digits of the number, the number decreases by 36.
10b + a = 10a + b - 36
Combine like terms
10b - b = 10a - a - 36
9b = 9a - 36
simplify, divide by 9
b = a - 4
-a + b = -4
:
use elimination on the two equation
a + b = 10
-a + b = -4
------------------addition eliminates a, find b
2b = 6
b = 3
You should be able to find a, and check that it satisfies the the statement
"On reversing the digits of the number, the number decreases by 36. "
then answer the question
" What is the product of the two digits ?"
|
Mixture_Word_Problems/696825: the number of hours that were left in the day was one-third of the number of hours already passed. how many hours were left in the day ?
1 solutions
Answer 429358 by ankor@dixie-net.com(15746) on 2012-12-25 15:43:32 (Show Source):
You can put this solution on YOUR website!the number of hours that were left in the day was one-third of the number of hours already passed.
how many hours were left in the day ?
:
let x = no. hr left in the day
:
x =  (24-x)
Get rid of the fraction, mult by 3, resulting in
3x = 24 - x
3x + x = 24
4x = 24
x = 24/4
x = 6 hrs
|
Rate-of-work-word-problems/696722: 'A' can complete a work in 6 days and 'B' in 5 days. They work together with their full capacities and receive rs 220 as wages for the work. What is The share of 'B'
1 solutions
Answer 429263 by ankor@dixie-net.com(15746) on 2012-12-24 10:53:03 (Show Source):
You can put this solution on YOUR website! 'A' can complete a work in 6 days and 'B' in 5 days.
They work together with their full capacities and receive rs 220 as wages for the work.
What is The share of 'B'
:
Let b = B's amt
then
(220-b) = A's amt
:
An inverse relationship here
 = 
Cross multiply
5b = 6(220-b)
5b = 1320 - 6b
6b + 5b = 1320
11b = 1320
b = 1320/11
b = $120 is B's share
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Money_Word_Problems/696597: I am trying to create an algebra equation for a refinance dilemma.
I currently have a $150,000 balance of my mortgage for 20 more years at 3.8% APR. I am getting offers to refinance for 3.5% with $3600 closing or 3.3% APR with $4800 closing.
I am looking to use an algebra equations to determine how long it would take me to get my closing cost back and what company would be the best to use if I decide to do it.
Thanks
1 solutions
Answer 429244 by ankor@dixie-net.com(15746) on 2012-12-23 21:41:22 (Show Source):
You can put this solution on YOUR website!I currently have a $150,000 balance of my mortgage for 20 more years at 3.8% APR.
I am getting offers to refinance for 3.5% with $3600 closing or 3.3% APR with $4800 closing.
:
I would not refinance for small a difference in interest.
Your payment difference going from 3.8 to 3.3 is about $40 a month
To recover the cost of $4800 it would take you 120 months or 10 years
:
If you are paying $4800 up front just put it on the principal and reduce the life of the loan by almost a year (11 months)
11 monthly payments saved is a big amt
:
If you are not putting up front, they will add it to amt of the loan and of course charge you interest on it for 20 years
:
I think these finance companies are a bunch of crooks. Maybe a 2% reduction would make sense, but not .5 %
:
If you really want to save some money, put $500 or whatever you can on the principal every month, you would save enough money to pay cash for a car.
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Miscellaneous_Word_Problems/696669: The time, in hours, it takes to decorate the school gym for a dance varies inversely as the number of students, , who are helping decorate. If a group of 7 students can decorate the gym in 7 hours, which of the following equations best models the time, , it will take a group of students to decorate the gym?
1 solutions
Answer 429243 by ankor@dixie-net.com(15746) on 2012-12-23 21:16:10 (Show Source):
You can put this solution on YOUR website!The time, in hours, it takes to decorate the school gym for a dance varies inversely as the number of students, , who are helping decorate.
t =  , where
t = time in hrs
s = no. of students
k = constant of variation
:
If a group of 7 students can decorate the gym in 7 hours,
Find k
7 = 
k = 49
: which of the following equations best models the time, , it will take a group of students to decorate the gym?
t = 
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Travel_Word_Problems/696357: Use the verticle height formula to solve the following h= -16t^ + intitial velocity + initial height. A person throws a ball in the air with an initial height of 4 feet and an initial velocity of 40 feet per second. The person catches the ball when it is 3 feet from the ground. how much time is the ball in the air?
1 solutions
Answer 429240 by ankor@dixie-net.com(15746) on 2012-12-23 21:06:46 (Show Source):
You can put this solution on YOUR website! Use the vertical height formula to solve the following h= -16t^ + initial velocity + initial height.
A person throws a ball in the air with an initial height of 4 feet and an initial velocity of 40 feet per second.
The person catches the ball when it is 3 feet from the ground.
how much time is the ball in the air?
:
The equation for this situation:
-16t^2 + 40t + 4 = 3
-16t^2 + 40t + 4 - 3 = 0
-16t^2 + 40t + 1 = 0
Use the quadratic formula:
 . where
x = t; a = -16; b = 40; c = 1
:
:
Two solutions
t = 
t = -.024755; not a reasonable solution
and
t = 
t = +2.52 seconds is the time it is in the air and caught
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test/696666: Solve for x: 3^2x=27^x+1
2. Solve for x: 25^x-1=125^x
3.Solve for x: 16^x-2=(1/8)^x
Please help me.We didn't even learn any of this is class and I don't know to how solve it or start it. Please help. Step by step procedure will be helpful. Thanks in advance!
1 solutions
Answer 429217 by ankor@dixie-net.com(15746) on 2012-12-23 19:14:52 (Show Source):
You can put this solution on YOUR website! Solve for x:
Note that we can write 27 as a power of 3, 27 = 3^3, so we have
both exponents are powers of 3, therefore we can write it
2x = 3(x+1)
2x = 3x + 3
-3 - 3x - 2x
-3 = x
:
You can check this on a calc
enter: 3^(2*-3) look at the result
enter: 27(-3+1) see that the result is the same
;
:
2. Solve for x:
The same situation here; 25 = 5^2 and 125 = 5^3, so we can write it
Both exponents are the power of the same number (5) therefore
2(x-1) = 3x
2x - 2 = 3x
-2 = 3x - 2x
-2 = x
:
Check this on your calc
enter 25^(-2-1)
enter 125^(-2)
:
:
3.Solve for x: 16^x-2=(1/8)^x
we can write both as powers of 2, 2^4 = 16 and recall that 1/8 = 2^-3
 = 
so we have
4(x-2) = -3x
4x - 8 = -3x
4x + 3x = + 8
7x = +8
x = 8/7
:
Check this
Enter: 16^((8/7)-2)
Enter: (1/8)^(8/7)
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Age_Word_Problems/696512: The sum of ages of mother and her daughter is 50 years.After 20 years mothers age will be twice as that of a daughters age.Find their present ages
1 solutions
Answer 429132 by ankor@dixie-net.com(15746) on 2012-12-22 21:16:16 (Show Source):
You can put this solution on YOUR website!The sum of ages of mother and her daughter is 50 years.
After 20 years, mothers age will be twice as that of a daughters age.
Find their present ages.
:
let m = Mom's present age
let d = daughter's
:
Write an equation for each statement:
:
"The sum of ages of mother and her daughter is 50 years."
m + d = 50
:
"After 20 years mothers age will be twice as that of a daughters age."
m + 20 = 2(d + 20)
m + 20 = 2d + 40
m - 2d = 40 - 20
m - 2d = 20
:
Use elimination on these two equations
m + d = 50
m -2d = 20
---------------subtraction eliminates m, find d
3d = 30
d = 10 yrs is the daughter
:
I'll let you find Mom's age, check the solution in the last statement
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Numbers_Word_Problems/696513: If a set of markers is placed in rows of 4 each, there are 2 markers left over, if in rows of 5 each, there are 3 left over, and if in the rows of 7 there are 5 left over. What is the smallest number of markers that the set could contain?
1 solutions
Answer 429129 by ankor@dixie-net.com(15746) on 2012-12-22 21:08:40 (Show Source):
You can put this solution on YOUR website!If a set of markers is placed in rows of 4 each, there are 2 markers left over,
if in rows of 5 each, there are 3 left over, and if in the rows of 7 there are 5 left over.
What is the smallest number of markers that the set could contain?
:
We know from the statement "if in rows of 5 each, there are 3 left over," that the last digit has to be an 8, and from the 1st statement, not evenly divisible by 4.
I came up with a minimum of 138 markers
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Age_Word_Problems/696515: one grandpa, one dad, one grandson. total age of these three is 140yrs. grandsons age in months is eqaul to the age of grandpa n years and grandsons age in days is eqaul to the age of the dad in weeks. so what is the age of these three persons?
1 solutions
Answer 429067 by ankor@dixie-net.com(15746) on 2012-12-22 08:25:58 (Show Source):
You can put this solution on YOUR website!one grandpa, one dad, one grandson. total age of these three is 140yrs.
grandsons age in months is equal to the age of grandpa n years,
and grandsons age in days is equal to the age of the dad in weeks.
so what is the age of these three persons?
:
let a = grandpa's age (yrs)
let b = dad's age
let c = grandson's age
:
Write an equation for each statement:
:
"one grandpa, one dad, one grandson. total age of these three is 140yrs."
a + b + c = 140
:
" grandsons age in months is eqaul to the age of grandpa n years"
a = 12c
:
"and grandsons age in days is eqaul to the age of the dad in weeks."
52b = 365c
b =  c
:
Substitue for a and b in the 1st equation
12c + c + c = 140
13c + c = 140
mult by 52
52(13c) + 365c = 52(140)
676c + 365c = 7280
1041c = 7280
c = 7280/1041
c ~ 7 yrs old the grandson
How about grandpa?
12 * 7 = 84 yrs old is grandpa
and
Find Dad's age, using the total yrs equation
140 - 7 - 84 = 49 is dad's age
:
:
Check this
52(49) = 365(7)
divide both sides by 7
52*7 = 365
364 ~ 365, close enough?
:
so what is the age of these three persons? 84, 49, 7
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Travel_Word_Problems/696486: Please help me solve this word problem: A man drove his car 132 miles before the water pump broke. Then the car was pushed 1 mile to a gas station. THe man could drive the car 12 times faster than it could be pushed. If the total trip took 3 hours, find how fast the car was pushed.
I must incorporate the formula r=d/t
Which out of the variables r,d,t are equal? It seems as though it is the d variable because the car could be pushed 1 mile or driven 1 mile. I do not understand how to set up this equation using rationals.
1 solutions
Answer 429057 by ankor@dixie-net.com(15746) on 2012-12-21 21:56:32 (Show Source):
You can put this solution on YOUR website! A man drove his car 132 miles before the water pump broke.
Then the car was pushed 1 mile to a gas station.
THe man could drive the car 12 times faster than it could be pushed.
If the total trip took 3 hours, find how fast the car was pushed.
:
let r = the speed the car can be pushed
then
12r = the speed the car is driven
:
Write a time equation; time = dist/rate (t = d/r)
:
Drive time + push time = 3 hrs
 +  = 3
multiply by 12r to clear the denominators, results:
132 + 12(1) = 12r(3)
144 = 36r
r = 144/36
r = 4 mph is the pushing speed
:
:
See if that checks out; find the time of each
Drove:132/(12*4) = 2.75 hrs
Pushed: 1/4 = .25 hrs
-----------------------
total time = 3 hrs
:
:
Did all this make sense to you?
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Equations/696441: Solve the equation: x^2+y^2=34, x+y=2
1 solutions
Answer 429055 by ankor@dixie-net.com(15746) on 2012-12-21 21:27:27 (Show Source):
You can put this solution on YOUR website! Solve this system of equations:
x^2 + y^2 = 34
x + y = 2
y = (2-x)
:
Replace y in the 1st equation with (2-x)
x^2 + (2-x)^2 = 34
FOIL (2-x)(2-x)
x^2 + 4 - 4x + x^2 = 34
combine like terms
2x^2 - 4x + 4 - 34 = 0
2x^2 - 4x - 30 = 0
Simplify, divide by 2
x^2 - 2x - 15 = 0
Factors to
(x-5)(x+3) = 0
two solutions
x = 5, then y = -3
and
x = -3, the y = +5
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Pythagorean-theorem/696349: Imagine that you are a pirate on watch in a crow's nest so that your eyes are 40 feet above the water. Determine the farthest distance from which you could spot the top of a 50 foot tree on a sea-level island.
1 solutions
Answer 429053 by ankor@dixie-net.com(15746) on 2012-12-21 21:07:45 (Show Source):
You can put this solution on YOUR website! Imagine that you are a pirate on watch in a crow's nest so that your eyes are 40 feet above the water.
Determine the farthest distance from which you could spot the top of a 50 foot tree on a sea-level island.
:
Use the distance (in miles) to horizon formula: d =  ; (h in ft)
Add the height of the crows nest and tree: 90 ft
d = 
d = 11.6 miles
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Mixture_Word_Problems/695784: Mrs. Thomas walked 160 feet on a moving walkway in 40 seconds. Against the walkway she was able to walk the same distance in 80 seconds. What is the rate of the escalator? (How fast)
What is Mrs. Thomas' normal rate? (How fast)
1 solutions
Answer 429051 by ankor@dixie-net.com(15746) on 2012-12-21 20:45:03 (Show Source):
You can put this solution on YOUR website!Mrs. Thomas walked 160 feet on a moving walkway in 40 seconds.
Against the walkway she was able to walk the same distance in 80 seconds.
What is the rate of the escalator? (How fast)
What is Mrs. Thomas' normal rate? (How fast)\
:
let w = the normal walking rate
let e = the escalator rate
then
(w+e) = the effective rate walking with the escalator
and
(w-e) = the effective rate walking against the escalator
:
Write a distance equation for each scenario
:
40(w+e) = 160
and
80(w-e) = 160
:
Simplify both equation; divide the 1st one by 40, the 2nd one by 80, results:
w + e = 4
w - e = 2
-----------adding eliminates e find w
2w = 6
w = 3 ft/sec is the normal walk rate
then
3 + e = 4
e = 4 -3
e = 1 ft/sec is the escalator rate
:
:
You can confirms this in both original equations
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Rate-of-work-word-problems/696478: Suppose I paint a wall in 10 hours, and you and I together paint a wall in 2 hours. How much faster do you paint a wall than I?
1 solutions
Answer 429046 by ankor@dixie-net.com(15746) on 2012-12-21 19:21:45 (Show Source):
You can put this solution on YOUR website! Suppose I paint a wall in 10 hours, and you and I together paint a wall in 2 hours.
How much faster do you paint a wall than I?
:
Let t = time for you to paint the wall
:
Let the completed job = 1 (A painted wall)
:
A shared work equation
 +  = 1
Multiply by 10t, results
2t + 10(2) = 10t
20 = 10t - 2t
20 = 8t
t = 20/8
t = 2.5 hrs
:
10 - 2.5 = 7.5 hrs faster
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Linear_Equations_And_Systems_Word_Problems/696362: Please answer my question: If 6 kilos of oranges and 5 kilos of apples cost 419 while 5 kilos of oranges and 7 kilos of apples cost 488, what is the cost of each per kilo?
1 solutions
Answer 429043 by ankor@dixie-net.com(15746) on 2012-12-21 19:05:30 (Show Source):
You can put this solution on YOUR website!If 6 kilos of oranges and 5 kilos of apples cost 419 while 5 kilos of oranges
and 7 kilos of apples cost 488, what is the cost of each per kilo?
:
Let x = cost of oranges per kilo
Let y = cost of apples
:
write an equation for each transaction
6x + 5y = 419
5x + 7y = 488
:
Use elimination here, mult the 1st eq by 7 and the 2nd eq by 5
42x + 35y = 2933
25x + 35y = 2440
-------------------subtraction eliminates y, find x
17x = 493
x = 493/17
x = 29 is the cost of the oranges
;
You can find the cost of the apples, substitute 29 for x in one of the equations and find y.
Check your solutions in the other equation.
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Polynomials-and-rational-expressions/696359: Steve is two thirds as old as Alex. In seven years, Steve will be three fourths as old as Alex. How old are they now?
1 solutions
Answer 429021 by ankor@dixie-net.com(15746) on 2012-12-21 16:48:09 (Show Source):
You can put this solution on YOUR website!Steve is two thirds as old as Alex.
In seven years, Steve will be three fourths as old as Alex.
How old are they now?
:
let s = Steve's present age
Let a = Alex's age
:
Write an equation for each statement
:
"Steve is two thirds as old as Alex."
s =  a
get rid of the fraction, mult both side by 3
3s = 2a
3s - 2a = 0
:
" In seven years, Steve will be three fourths as old as Alex."
s + 7 =  (a+7)
mult both sides by 4
4(s+7) = 3(a + 7)
4s + 28 = 3a + 21
4s - 3a = 21 - 28
4s - 3a = -7
:
Use elimination here, mult the 1st equation by 3, the 2nd equation by 2
9s - 6s = 0
8s - 6a = -14
---------------subtraction eliminates a, find s
s = 14 yrs is Steve's age
then
3(14) - 2(a) = 0
42 - 2a = 0
-2a = -42
a = 21 yrs is Alex's age
;
:
Confirm this in the statement:
"In seven years, Steve will be three fourths as old as Alex."
14 + 7 = (21+7)
21 = (28)
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