Question 152437: You participate in a triathlon in which you swam three miles, ran five miles and then bicycled ten miles. You ran twice as fast as you swam and cycled three times as fast as you swam. If your total time was one hour and forty-six minutes, how fast did you swim?
Answer by orca(409)   (Show Source):
You can put this solution on YOUR website! Suppose you swam at x miles per hour.
Then you ran at 2x miles per hour, and cycled at 3x miles per hour.
Time spent on swimming: 3/x
Time spent on running: 5/(2x)
Time spent on cycling: 10/(3x)
The total time spent is: 3/x + 5/(2x) + 10/(3x)
As the total time was one hour and forty-six minutes, we can set up an equation:
3/x + 5/(2x) + 10/(3x) = 1 + 46/60
Solving for x, we have
18/(6x) + 15/(6x) + 20/(6x) = 53/30
53/(6x) = 53/30
1/(6x) = 1/30
6x = 30
x = 5
So he swam at 5 miles per hour.
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