Chapter A.8, Problem 51AYU

To determine

To find: What is the distance of the run? What is the distance of the bicycle race?

Answer to Problem 51AYU

12 miles of run and 75 miles of bicycle.

Explanation of Solution

Given:

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.

Calculation:

Run data:

$\text{Rate }=6\text{ mph};\text{ time}=x\text{hours};\text{ distance }=6x\text{miles}$.

Bike data:

Rate = 25 mph; time $=5-x$ hours; distance $=25\left(5-x\right)$ miles.

Equation:

Distance $+$ Distance $=87$

$6x+25\left(5\right)-25x=87$

$-19x=-38$

$x=2 \text{hrs}$

Therefore $6x=12$ miles of running. Then

$87-12=75$ miles of bicycle race.