SOLUTION: A bicylist and a hiker leave the same place at the same time and travel in the same direction: the bicylist travels three times as fast as the hiker. At the end of 3 hr they are

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Question 145497: A bicylist and a hiker leave the same place at the same time and travel in the same direction: the bicylist travels three times as fast as the hiker. At the end of 3 hr they are 24 miles apart. HOw fast does the hiker travel?
Answer by solver91311(24713) About Me  (Show Source):
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At the end of 3 hours, the hiker has traveled d miles and the bicyclist has traveled d%2B24 miles. The hiker's speed is r%5Bh%5D and the bicyclist's speed is r%5Bb%5D=3r%5Bh%5D. The time traveled, 3 hours, is the same for both.

We know that d=rt in general, so in general, t=d%2Fr.

For the hiker: d%2Fr%5Bh%5D=3 and for the bicyclist: %28d%2B24%29%2F%283r%5Bh%5D%29=3, so

Since d%2Fr%5Bh%5D=3, we can write d=3r%5Bh%5D and substitute this value for d into %28d%2B24%29%2F%283r%5Bh%5D%29=3, making %283r%5Bh%5D%2B24%29%2F%283r%5Bh%5D%29=3 or 3r%5Bh%5D%2B24=9r%5Bh%5D

Now all that needs to be done is to solve that last equation for r%5Bh%5D, and I will leave that part as an exercise for the student.