SOLUTION: Karin can run 3 miles per hour faster than her sister Kim can walk. If Karin ran 12 miles in the same time it took Kim to walk 8 miles, what is the speed of each sister in this ca

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Question 1137496: Karin can run 3 miles per hour faster than her sister Kim can walk. If Karin ran 12 miles in the same time it took Kim to walk 8 miles, what is the speed of each sister in this case?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the Kim's rate (the slower sister) in miles per hour.

Then the faster sister's rate is (x+3) miles per hour.



Karin spent 12%2F%28x%2B3%29 hours running.

Kim    spent  8%2Fx  hours walking.



The condition says


    12%2F%28x%2B3%29 = 8%2Fx.


It is your basic equation.

It is called "time" equation, because its both sides represent time spent.



To solve the equation, cross multiply.  You will get


    12x = 8((x+3)

    12x = 8x + 24

    12x - 8x = 24

     4x      = 24

      x      = 24/4 = 6.


Answer.  Kim's rate is 6 miles per hour;  Karin's rate is 6+3 = 9 miles per hour.

Solved.

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From my solution learn how to use, how to write and how to solve a "time" equation.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a way to set up the problem which is different from the solution from the other tutor.

Let Kim's speed be x; then Karin's speed is x+3.

Since the times are the same, the ratio of speeds is the same as the ratio of distances. So

%28x%2B3%29%2Fx+=+12%2F8+=+3%2F2
2%28x%2B3%29+=+3x
2x%2B6+=+3x
6+=+x

Kim's speed is x = 6mph; Karin's speed is x+3 = 9mph