PreCalculus Algebra Word Question

Question

Suppose you have entered a 97 mile biathlon that consists of a run and bicycle race. During your run, your average velocity is 8 miles per hour, and during your bicycle race, your average velocity is 27 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 ?

Answer 1

Let x be the run time and y be the cycle time

x + y = 5 (as total time = 5 hr)

8x + 27y = 97 (as distance = ave velocity x time)

-8x - 8y = -40 (first equation x (-8)) Now we add eqn 2 and 3

19 y = 57, so y = 3

If y = 3, x = 2

Answer 2