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2r-2/ r^2+3r-28 + 4/r+7 = r/r-4
This should read 2r-2 over r squared plus 3r minus 28 plus 4 over r+7 equals 1 over r-4.
1 solutions
Answer 353845 by ankor@dixie-net.com(15746)   on 2011-12-02 21:38:41 (Show Source):
You can put this solution on YOUR website!
I am assuming the last fraction is 1/(r-4) as you said in the text
:
 +  = 
Factor the 1st denominator and this will all make sense
 + =
Multiply by (r+7)(r-4), cancels the denominators and you have
2r - 2 + 4(r-4) = r + 7
2r - 2 + 4r - 16 = r + 7
6r - 18 = r + 7
6r - r = 7 + 18
5r = 25
r = 25/5
r = 5
You can check this solution in the original equation
|
Rate-of-work-word-problems/540713: City A and City B are 135 km away. Two cars drove from A to B. The first car left 5 hours earlier. The second car arrived City B 30 minutes later than the first one. If the ratio of the speed of the first to the speed of the second car is 2:5, find the speed of the first car.
1 solutions
Answer 353840 by ankor@dixie-net.com(15746) on 2011-12-02 21:11:58 (Show Source):
You can put this solution on YOUR website!City A and City B are 135 km away. Two cars drove from A to B.
The first car left 5 hours earlier.
The second car arrived City B 30 minutes later than the first one.
If the ratio of the speed of the first to the speed of the second car is 2:5, find the speed of the first car.
:
Let t = travel time of the 1st car
then
t - 5 + .5 = (t-4.5) is the travel time of the 2nd car (left 5 hrs later, arrived a half hr later
:
speed = dist/time
:
 = the speed of the 1st car
and
 = the speed of the 2nd car
the ratio of the speeds is 2:5
:
------------- = 
:
Cross multiply
5 = 2
:
 = 
Cross multiply
675(t-4.5) = 270t
675t - 3037.5 = 270t
675t - 270t = 3037.5
405t = 3037.5
t = 
t = 7.5 hrs for the 1st car to make the trip
then
7.5 - 4.5 = 3 hrs for the 2nd car.
:
Find the speed of the 1st car
 = 18 mph
:
Find the speed of the 2nd car to check our solution
 = 45 mph
:
See if the  = ; both equal .4
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Rate-of-work-word-problems/540710: Brain and David can finish the job in 12 days if they work together. If only one of them works on a job, David will take 10 days longer than Brain. How many days does David need to finish the job alone?
1 solutions
Answer 353831 by ankor@dixie-net.com(15746) on 2011-12-02 20:28:22 (Show Source):
You can put this solution on YOUR website!Brain and David can finish the job in 12 days if they work together.
If only one of them works on a job, David will take 10 days longer than Brain.
How many days does David need to finish the job alone?
:
Let t = time required by Brian working alone
then
(t+10) = time required by David
:
Let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
:
 +  = 1
multiply by t(t+10), results:
12(t+10) + 12t = t(t+10)
12t + 120 + 12t = t^2 + 10t
24t + 120 = t^2 + 10t
0 = t^2 + 10t - 24t - 120
A quadratic equation
t^2 - 14t - 120 = 0
(t-20)(t+6) = 0
the positive solution
t = 20 days for Brian to do the job
I'll let you figure out how many days that David will required
|
Rate-of-work-word-problems/540723: Two men, working full time, paint a room in 8 hours. How long would it take five men to paint the same room full time at the same rate?
1 solutions
Answer 353827 by ankor@dixie-net.com(15746) on 2011-12-02 20:13:05 (Show Source):
You can put this solution on YOUR website!Two men, working full time, paint a room in 8 hours.
Find how many man-hrs to complete the job:
2 * 8 = 16 man-hrs
:
How long would it take five men to paint the same room full time at the same rate?
let h = no. of hrs for 5 men to do the job
5h = 16
h = 16/5
h = 3.2 hrs
|
Rectangles/540676: the length of a rectangle is 3 less than twice the width. if the perimeter is 72cm, what is the lenght of the rectangle? im trying to help my son with his homework and dont know how to explain this
1 solutions
Answer 353803 by ankor@dixie-net.com(15746) on 2011-12-02 18:34:57 (Show Source):
You can put this solution on YOUR website!the length of a rectangle is 3 less than twice the width. if the perimeter is 72cm, what is the lenght of the rectangle?
:
Write an equation for each statement:
"the length of a rectangle is 3 less than twice the width. "
L = 2W - 3
:
"the perimeter is 72cm,"
2L + 2W = 72
This eq can be simplified, divide thru by 2
L + W = 36
:
From the 1st statement, replace L with (2W-3) in the above equation
(2W-3) + W = 36
add 3 to both sides
2W - 3 + 3 + W = 36 + 3
3W = 39
divide both sides by 3
W = 13 is the width
then
L = 2W - 3
L = 2(13) - 3
L = 26 - 3
L = 23 is length
:
:
Check this in the perimeter equation
2(23) + 2(13) =
46 + 26 = 72
|
Travel_Word_Problems/540103: how long would it take for a car go in 120ft at 70miles per hour?
how long it take to go 120 ft at 55mph?
1 solutions
Answer 353799 by ankor@dixie-net.com(15746) on 2011-12-02 18:18:05 (Show Source):
You can put this solution on YOUR website!how long would it take for a car go in 120ft at 70 miles per hour?
Find the no. of ft/sec at 70 mph, divide that into 120
 = 102.667 ft/sec
:
 = 1.1688 sec to go 120 ft
:
how long it take to go 120 ft at 55mph?
Do it the same way, replace 70 with 55
:
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Volume/540398: Exactly how many cubic inches can an ice cream cone hold(within the cone) if its height is 4 inches and the radius of its base is 1.5 inches? Include correct units with your solution. The only answer Im coming up with is 6 cub in and Im thinking its wrong please help.
1 solutions
Answer 353789 by ankor@dixie-net.com(15746) on 2011-12-02 15:31:08 (Show Source):
You can put this solution on YOUR website!Exactly how many cubic inches can an ice cream cone hold(within the cone) if its height is 4 inches and the radius of its base is 1.5 inches?
:
V =  *  is the volume of a cone
V = * 
V = 9.425 cu/inches
|
Triangles/540402: Hi, I'm stuck on this problem. Could someone please help me solve it? I appreciate it. Thank you.
The ratio of the segments into which the altitude the to the hypotenuse of a right triangle divides the hypotenuse is 9 : 4. What is the length of the altitude?
A. 3
B. 6
C. 36
D. Cannot be determined
Thank you!
1 solutions
Answer 353778 by ankor@dixie-net.com(15746) on 2011-12-02 13:44:42 (Show Source):
You can put this solution on YOUR website!The ratio of the segments into which the altitude the to the hypotenuse of a right triangle divides the hypotenuse is 9 : 4.
What is the length of the altitude?
:
Cannot be determined, the ratio will help you solve the angles, but will not give the actual lengths of the sides
|
Miscellaneous_Word_Problems/540553: A military plane carrying heavy cargo can fly at an average rate of 400 mph. Another plane carrying soldiers can fly at an average rate of 600 mph. Both planes leave the same airbase at the same time and are headed to the same destination. If the cargo plane took two and a half hours longer to arrive at the destination than the plane carrying soldiers, then how far is the destination?
1 solutions
Answer 353774 by ankor@dixie-net.com(15746) on 2011-12-02 13:33:36 (Show Source):
You can put this solution on YOUR website!A military plane carrying heavy cargo can fly at an average rate of 400 mph.
Another plane carrying soldiers can fly at an average rate of 600 mph.
Both planes leave the same airbase at the same time and are headed to the same destination.
If the cargo plane took two and a half hours longer to arrive at the destination than the plane carrying soldiers, then how far is the destination?
:
Let t = travel time of the 600 mph plane
then
(t+2.5) = travel time of the 400 mph
:
Write a distance equation: dist = speed * time
Both planes travel the same distance
:
600t = 400(t+2.5)
600t = 400t + 1000
600t - 400t = 1000
200t = 1000
t = 1000/200
t = 5 hrs for the fast plane
:
Find the distance
600*5 = 3000 mi
:
Check the distance using the slower plane which traveled for 7.5 hr
400*7.5 = 3000 mi, confirms our distance
|
Evaluation_Word_Problems/540215: Five times a number minus twice another number equals twenty-two. The sum of the numbers is three. Find the numbers.
1 solutions
Answer 353739 by ankor@dixie-net.com(15746) on 2011-12-02 08:47:42 (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement
;
Five times a number minus twice another number equals twenty-two.
5x - 2y = 22
:
The sum of the numbers is three.
x + y = 3
y = (3-x); use this form for substitution
:
Substitute (3-x) for y in the 1st equation
5x - 2(3-x) = 22
5x - 6 + 2x = 22; you have to change the sign of -x when you mult it by -2
5x + 2x = 22 + 6
7x = 28
x = 28/7
x = 4
find y
y = 3 - 4
y = -1
:
Our solution, x=4, y =-1
:
Check these solutions in the 1st statement:
Five times a number minus twice another number equals twenty-two.
5(4) - 2(-1) =
20 + 2 = 22; confirms our solutions
|
Linear_Algebra/540293: Can you help me with the constraints on this linear programming question?
A tourist agency can sell up to 1200 travel packages for a football game. The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers. The agency can locate no more than 10 planes for the travel packages. Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.
Please and Thank You.
1 solutions
Answer 353671 by ankor@dixie-net.com(15746) on 2011-12-01 22:02:48 (Show Source):
You can put this solution on YOUR website!A tourist agency can sell up to 1200 travel packages for a football game.
The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight.
The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers.
The agency can locate no more than 10 planes for the travel packages.
Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900.
Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.
:
Let x = number of 150 passenger planes
Let y = number of 100 passenger planes
:
Number of airplanes:
x + y =< 10
Put in the general (y=) form, to plot on a graph
y =< 10 - x; (purple line)
:
Number of travel packages sold:
150x + 100y =< 1200
100y =< 1200 - 150x
y =< 1200/100 - (150/100)x
y =< 12 - 1.5x; (green line)
:
The graph:
:
Feasibility region is at or below the purple or green lines whichever is lowest
:
The vertices:
x = 8, y = 0
x = 0, y = 10
Solve the two equation system to find the other vertici
150x + 100y = 1200
Simplify, divide by 100
1.5x + y = 12
x + y = 10
----------------subtract, find x
.5x = 2
x = 2/.5
x = 4
:
Find y:
4 + y = 10
y = 6
The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes
:
Revenue:
4*150*1200 = $720,000
6*100*900 = $540,000
--------------------
total is $1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes
But
Max revenue would be 8 full 150 pass planes, forget the 100 pass planes
8 * 150 * 1200 = $1,440,000
|
Miscellaneous_Word_Problems/540282: The average weight of the first two dogs was 43 pounds. The average weight of the next three dogs was 58 pounds. What was the average weight of all the dogs?
I can't figure out how to do this problem. I added the numbers and divided by 5 and got 20.2 but the teacher marked it wrong. I have to turn it in corrected tomorrow.Thanks for any help you can provide.
1 solutions
Answer 353629 by ankor@dixie-net.com(15746) on 2011-12-01 20:17:23 (Show Source):
You can put this solution on YOUR website!The average weight of the first two dogs was 43 pounds.
The average weight of the next three dogs was 58 pounds.
What was the average weight of all the dogs?
:
Try it this way
Av = 
Av = 
Av = 
Av = 52 lbs
|
Quadratic_Equations/540037: I have two questions both on quadratic equations. I am not understanding how to do them. The first one says to write it in standard quadratic form. The solutions are
negative sign sqrt 5, and 4 sqrt 5.
The second one says to find the solution(s).
w^4-20w^2-2=0.
If you could help with either of these I would greatly appriciate it.
Thanks so much!
1 solutions
Answer 353593 by ankor@dixie-net.com(15746) on 2011-12-01 17:49:23 (Show Source):
You can put this solution on YOUR website!The first one says to write it in standard quadratic form. The solutions are
negative sign sqrt 5, and 4 sqrt 5.
:
x =  is derived from the factor (x +  )
and
x =  is derived from the factor (x - )
FOIL
(x - )(x + ) = x^2 + x - x - 4(5)
:
x^2 -  x - 20, is the quadratic equation for these solutions
:
:
The second one says to find the solution(s).
w^4 - 20w^2 - 2 = 0.
Use the quadratic formula to find w^2
x = w^2, a=1, b=-20, c=-2
:
Two solutions
 = +/- 
w = +4.4833
and
w = -4.4833, these are only real solutions to this
the other solution will be square root of a negative number
|
Numbers_Word_Problems/539571: There are 72 members of the choir. There are 6 more boys than girls in the choir.
a. Write the model of a system for the above situation.
b. Do you need to multiply any of the equations by a constant before solving by elimination? Explain.
Thank you!!!
1 solutions
Answer 353588 by ankor@dixie-net.com(15746) on 2011-12-01 15:20:57 (Show Source):
You can put this solution on YOUR website!There are 72 members of the choir. There are 6 more boys than girls in the choir.
a. Write the model of a system for the above situation.
:
Write an equation for each statement
"There are 72 members of the choir."
b + g = 72
"There are 6 more boys than girls"
b = g + 6
Since you want to use elimination, write like this
b - g = 6
:
b. Do you need to multiply any of the equations by a constant before solving by elimination? Explain.
No
b + g = 72
b - g = 6
-----------adding eliminates g, find b
2b = 78
b = 78/2
b = 39 boys
then
39 + g = 72
g = 72 - 39
g = 33 girls
:
Check the solutions in original equations
|
Triangles/539462: Find the length of the leg of an isosceles triangle whose perimeter is 64 and altitude is 8.
P.S: Can you please explain how to solve this when giving the answer? Thanks!
1 solutions
Answer 353578 by ankor@dixie-net.com(15746) on 2011-12-01 13:08:59 (Show Source):
You can put this solution on YOUR website!Find the length of the leg of an isosceles triangle whose perimeter is 64 and altitude is 8.
:
Let x = the length of one of the equal sides
then
(64-2x) = the length of the 3rd side
(32-x) = half the length of the 3rd side
:
Two right triangles are formed with the altitude, half the 3rd side and the one leg of the equal side will be the hypotenuse (x)
:
x^2 = 8^2 + (32-x)^2
x^2 = 64 + 1024 - 64x + x^2
x^2 = 1088 - 64x + x^2
x^2 - x^2 + 64x = 1088
64x = 1088
x = 
x = 17 is the length of the equal sides
then
64 - 2(17) = 30 is the length of the 3rd side
:
:
Confirm this, find the altitude (a)
a = 
a = 8
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Travel_Word_Problems/539518: A dealer mixed coffee worth 85 cents per pound with cofee worth 55 cents per pound. How many pounds of each kind did he use to make a mixture of 120 pounds to sell at 75 cents per pound?
please include explanation (step by step) im so confused!
1 solutions
Answer 353507 by ankor@dixie-net.com(15746) on 2011-11-30 21:54:51 (Show Source):
You can put this solution on YOUR website!A dealer mixed coffee worth 85 cents per pound with coffee worth 55 cents per pound.
How many pounds of each kind did he use to make a mixture of 120 pounds to sell at 75 cents per pound?
:
Let x = amt of 85 cent coffee required
the total is to be 120, therefore
(120-x) = amt of 55 cent coffee
:
A typical mixture equation, we can solve it using cents
:
85x + 55(120-x) = 75(120)
85x + 6600 - 55x = 9000
85x - 55x = 9000 - 6600
30x = 2400
x = 2400/30
x = 80 lb of 85 cent coffee
then
120 - 80 = 40 lb of 55 cent coffee
:
:
Confirm our solution in the original mixture equation
85(80) + 55(40) = 75(120)
6800 + 2200 = 9000
:
Was this step-by-step enough for you, any questions on this?
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Numbers_Word_Problems/539590: For the fundraiser, Will sold 225 candy bars. He earns $1 for each almond candy bar he sells and $0.75 for each caramel candy bar he sells. If he earned a total of $187.50, how many of each type of candy bar did he sell for the fundraiser.
Thanks you so much!!!
1 solutions
Answer 353505 by ankor@dixie-net.com(15746) on 2011-11-30 21:40:08 (Show Source):
You can put this solution on YOUR website!Will sold 225 candy bars.
He earns $1 for each almond candy bar he sells and $0.75 for each caramel candy bar he sells.
If he earned a total of $187.50, how many of each type of candy bar did he sell for the fundraiser.
:
Let a = no. of almond candy bars
Let c = no. of caramel
:
"Will sold 225 candy bars."
a + c = 225
:
"He earns $1 for each almond candy bar he sells and $0.75 for each caramel candy bar he sells. If he earned a total of $187.50,"
1a + .75c = 187.50
:
We can use elimination here, easily
Subtract the above equation from the 1st equation
a + c = 225
a +.75c = 187.5
------------------subtraction eliminates a, find c
.25c = 37.5
c = 
c = 150 caramel bars
:
Find a using the 1st equation
a + 150 = 225
a = 225 - 150
a = 75 almond bars
:
:
Confirm this in the value equation
1(75) + .75(150) =
75 + 112.5 = 187.5
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Money_Word_Problems/539528: how many pounds of seed worth $1.05 per pound must be mixed with 60 pounds of seed worth $90 per pound in order to produce a mixture to sell for $1.00 per pound?
please show steps! it'd help a lot, thanks :D
1 solutions
Answer 353499 by ankor@dixie-net.com(15746) on 2011-11-30 21:30:18 (Show Source):
You can put this solution on YOUR website!how many pounds of seed worth $1.05 per pound must be mixed with 60 pounds of seed worth $.90 per pound in order to produce a mixture to sell for $1.00 per pound? (I added the decimal to $90)
:
Let x = amt of 1.05 seed required
then
(x+60) = the resulting mixture
:
Write typical mixture equation:
:
1.05x + .90(60) = 1(x+60)
1.05x + 54 = x + 60
1.05x - x = 60 - 54
.05x = 6
x = 
x = 120 lb of 1.05 seed required
:
:
Check the solution in the original equation
1.05(120) + .9(60) = 1(120+60)
126 + 54 = 180
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Travel_Word_Problems/539058: At noon, your family leaves Louisville on a trip to Memphis driving at 40 miles per hour. Your uncle leaves Memphis to come to Louisville 2 hours later. He is taking the same route and is driving 60 miles per hour. The two cities are 380 miles apart. At what time do the cars meet?
1 solutions
Answer 353492 by ankor@dixie-net.com(15746) on 2011-11-30 21:17:29 (Show Source):
You can put this solution on YOUR website!At noon, your family leaves Louisville on a trip to Memphis driving at 40 miles per hour.
Your uncle leaves Memphis to come to Louisville 2 hours later.
He is taking the same route and is driving 60 miles per hour.
The two cities are 380 miles apart. At what time do the cars meet?
:
Let t = your travel time
then
(t-2) = uncle's travel time who left two hours later
:
It helps to know that the sum of the distances of the two cars equal 380 mi
Write a distance equation, dist = speed * time
:
your dist + Unc's dist = 380 miles
40t + 60(t-2) = 380
40t + 60t - 120 = 380
40t + 60t = 380 + 120
100t = 500
t = 
t = 5 hrs is your travel time, you left at noon, therefore
you meet at 5 PM
:
:
We can confirm this by finding the distance that each traveled
40(5) = 200 mi
60(3) = 180 mi, (left 2 hrs later)
----------------
total = 380 mi
:
Did this make sense to you now?
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Rate-of-work-word-problems/539007: Rashard drives 100 mi from Detroit to Lansing, and later drives 90 mi more from Lansing to Grand Rapids. The trip from Lansing to Grand Rapids takes him a half hour less than the drive from Detroit to Lansing. What is his driving average speed if it is the same on both parts of the trip?
1 solutions
Answer 353451 by ankor@dixie-net.com(15746) on 2011-11-30 19:48:14 (Show Source):
You can put this solution on YOUR website!Rashard drives 100 mi from Detroit to Lansing, and later drives 90 mi more from Lansing to Grand Rapids.
The trip from Lansing to Grand Rapids takes him a half hour less than the drive from Detroit to Lansing.
What is his driving average speed if it is the same on both parts of the trip?
:
Let t = time from Det to Lan
then
(t-.5) = time from Lan to G.R.
:
Write a speed equation, speed = dist/time
Speed was the same on both trips
:
 = 
cross multiply
100(t-.5) = 90t
100t - 50 = 90t
100t - 90t = 50
10t = 50
t = 50/10
t = 5 hrs to Lansing
Find the speed
100/5 = 20 mph was his average speed
check the speed
90/4.5 = 20 mph
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Age_Word_Problems/539260: You are 4 years older than your brother. Two years ago, you were 1.5 times as old as he was. What is your present age?
1 solutions
Answer 353448 by ankor@dixie-net.com(15746) on 2011-11-30 19:38:23 (Show Source):
You can put this solution on YOUR website!You are 4 years older than your brother.
y = b + 4
:
Two years ago, you were 1.5 times as old as he was.
y - 2 = 1.5(b - 2)
y - 2 = 1.5b - 3
y = 1.5b - 3 + 2
y = 1.5b - 1
Replace y with (b+4) (from the 1st statement}
b + 4 = 1.5b - 1
b - 1.5b = - 1 - 4
-.5b = -5
b = 
b = +10 yrs is the brother's age
and
10 + 4 = 14 yrs is your age
:
See if that works in the 2nd statement
14 - 2 = 1.5(10-2)
12 = 1.5(8); confirms our solutions
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Geometry_Word_Problems/539441: The hypotenuse of a right triangle is four times then length of one of the legs. The length of the other leg is square root 735 feet. Find the length of the leg and hypotenuse.
1 solutions
Answer 353443 by ankor@dixie-net.com(15746) on 2011-11-30 19:26:40 (Show Source):
You can put this solution on YOUR website!The hypotenuse of a right triangle is four times then length of one of the legs.
let x = length of one leg
then
4x = length of the hypotenuse
:
The length of the other leg is square root 735 feet.
Find the length of the leg and hypotenuse.
:
x^2 +  = (4x)^2
which is:
x^2 + 735 = 16x^2
735 = 16x^2 - x^2
735 = 15x^2
divide both sides by 15
49 = x^2
x = 
x = 7 is one leg
then
4(7) = 28 is the hypotenuse
and
 ~ 27.111 ft is the other leg
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Geometry_Word_Problems/538994: The box has a volume of 12 cubic feet. If all three dimensions were doubled, how would that affect the volume of the new box relative to the orginal box? (would the volume be double, tripled...?)
a=3 feet b=2feet c=2feet.
1 solutions
Answer 353330 by ankor@dixie-net.com(15746) on 2011-11-30 09:56:46 (Show Source):
You can put this solution on YOUR website!The box has a volume of 12 cubic feet.
If all three dimensions were doubled, how would that affect the volume of the new box relative to the original box?
:
that would be 2^3, it increase the volume by a factor of 8
:
2*2*3 = 12 cu ft
4*4*6 = 96 cu ft
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Linear-systems/539093: At 10:00 am, a car leaves a home at a rate of 60 mi/h. At the same time, another care leaves the same home at a rate of 50 mi/h in the opposite direction. At what time will the cars be 330 miles apart?
1 solutions
Answer 353324 by ankor@dixie-net.com(15746) on 2011-11-30 09:09:47 (Show Source):
You can put this solution on YOUR website!At 10:00 am, a car leaves a home at a rate of 60 mi/h. At the same time, another care leaves the same home at a rate of 50 mi/h in the opposite direction.
At what time will the cars be 330 miles apart?
:
You can do this in your head, the relative speed of the two cars is the sum which is 110 mph, divide that into 330 and get 3 hrs, 1 PM is answer
:
However, they may want you to show some equations here
:
Let t = time for this to be true;
write a distance equation, dist = speed * time
60t + 50t = 330
solve for t
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Age_Word_Problems/539036: Sally and Garry's combined age is 39,27 years more than the combined age of Garry and Nora,which is 25 years less than Sally and Nora's combined age.In how many years'time will the sum of all their ages be 188.
1 solutions
Answer 353322 by ankor@dixie-net.com(15746) on 2011-11-30 08:42:35 (Show Source):
You can put this solution on YOUR website!Sally and Garry's combined age is 39, 27 years more than the combined age of Garry and Nora, which is 25 years less than Sally and Nora's combined age.
In how many years time will the sum of all their ages be 188?
:
"Sally and Garry's combined age is 39"
S + G = 39
:
"27 years more than the combined age of Garry and Nora,"
N + G = 39-27
N + G = 12
:
"which is 25 years less than Sally and Nora's combined age."
N + G = S + N - 25
subtract N from both sides
G = S - 25
:
Using the first equation, replace G with (S-25)
S + (S-25) = 39
2S = 39 + 25
2S = 64
S = 64/2
S = 32 is Sally's age
then
G + 32 = 39
G = 39 - 32
G = 7 yrs is Gary's age
:
Find N
N + G = 12
N + 7 = 12
N = 12 - 7
N = 5 yrs is Nora's age
:
:
Check solutions in the last equation
N + G = S + N - 25
5 + 7 = 32 + 5 - 25
12 = 37 - 25; confirms our solution of: G=7, S=32, N=5
:
"In how many years time will the sum of all their ages be 188?"
let y = no. of yrs for this to be true
(y+7) + (y+32) + (y+5) = 188
3y + 44 = 188
3y = 188 - 44
3y = 144
y = 144/3
y = 48 yrs
:
:
Check this:
(y+7) + (y+32) + (y+5) =
48+7 + 48+32 + 48+5 =
55 + 80 + 53 = 188
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Travel_Word_Problems/538840: a freight train left pennsylvania station traveling at 35mph. two hours later, a highspeed train left pennsylvania station on parallel tracks traveling 55mph. In how many hours after the slow train starts will the two trains meet?
1 solutions
Answer 353261 by ankor@dixie-net.com(15746) on 2011-11-29 20:59:10 (Show Source):
You can put this solution on YOUR website!a freight train left pennsylvania station traveling at 35mph. two hours later, a highspeed train left pennsylvania station on parallel tracks traveling 55mph.
In how many hours after the slow train starts will the two trains meet?
:
Let t = travel time of the freight
then
(t-2) = travel time of fast train
:
When the fast train catches the freight, they will have traveled the same distance
Write a dist equation, dist = speed * time
:
fast dist = slow dist
55(t-2) = 35t
55t - 110 = 35t
55t - 35t = 110
20t = 110
t = 110/20
t = 5.5 hrs for the freight to be caught
:
:
Check this by finding the distance of each, should be the same
35*5.5 = 192.5 mi
55*3.5 = 192.5
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