Suppose you have entered a 156mile biathlon that consists of

Suppose you have entered a 156-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 7 miles per hour, and during your bicycle race, your average velocity is 27 miles per hour. You finish the race in 8 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 156 -x covered by bicycle .

Time for run = x/7 ;Time covered by bicycle = (156 -x)/27

x/7 + (156 -x)/27 = 8

solve for x: ( 27x + 1092 - 7x) /189 =8

(20x +1092) = 1512

x = 420/20 = 21 miles by running

and 135 miles by bicycle