Question 1209001
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Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. 
During your run, your average speed is 6 miles per hour, and during your bicycle race, 
your average speed is 25 miles per hour. You finish the race in 5 hours. 
What is the distance of the run? What is the distance of the bicycle race?
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Let "t" be the time running, in hours.

Then the time cycling is (5-t) hours.


The total distance equation is 

    6t + 25(5-t) = 87  miles.


Simplify and find "t"

    6t + 125 - 25t = 87,

     125 - 87 = 25t - 6t

         38   =    19t

          t    =    38/19 = 2 hours.


So, you run 2 hours and cycle 5-2 = 3 hours.


The distance running is  6*2 = 12 miles.  The distance cycling is 25*3 = 75 miles.    <U>ANSWER</U>
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Solved.