Suppose you have entered a 57mile biathlon that consists of

Suppose you have entered a 57-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 8 miles per hour, and during your bicycle race, your average velocity 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??

Solution

Let x be the distance covered by run and 57 -x covered by bicycle .

Time for run = x/8 ;Time covered by bicycle = (57 -x)/25

x/8 +(57-x)/25 =5

solve for x: ( 25x + 456 -8x )/200 = 5

( 17x +456) = 1000

17x = 544

x = 32 miles by running

and 25 miles by bicycle