SOLUTION: Two cyclists start at the same point and travel in opposite directions. One travels 4 mph slower than the other. In 3 hours they 108 miles apart. Find how fast each cyclist is trav

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Question 1096219: Two cyclists start at the same point and travel in opposite directions. One travels 4 mph slower than the other. In 3 hours they 108 miles apart. Find how fast each cyclist is traveling.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
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Two cyclists start at the same point and travel in opposite directions. One travels b mph slower than the other. In t hours they d miles apart. Find how fast each cyclist is traveling.
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Given: system%28b=4%2Ct=3%2Cd=108%29

Find: system%28r%2Cr-b%29


%28r%2B%28r-b%29%29t=d
2r-b=d%2Ft
2r=d%2Ft%2Bb
highlight_green%28r=dt%2F2%2Bb%2F2%29

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "x" be the speed of the fastest cyclist in miles per hour.

Then the speed of the slower cyclist is (x-4) miles per hour.


In 3 hour the fastest cyclist will cover 3x miles, while the slower will cover 3*(x-4) miles.


The sum of distances is 108 miles.  It gives you an equation

3x + 3*(x-4) = 108.


Simplify and solve for x:

3x + 3x - 12 = 108,

6x = 108 + 12  ====>  6x = 120  ====>  x = 20.


Answer.  The fastest cyclist speed is 20 mph.  The slower cyclist speed is 20-4 = 16 mph.

For many other similar solved problems see the lessons
- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.