Could someone work this and explain it better?

Question

Suppose you have entered a 113-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 23 miles per hour. You finish the race in 7 hours. What is the distance of the run? What is the distance of the bicycle race?

Answer 1

Hi Luke,

 

This is a classic example of distance-time-velocity relationship.

Let's assume the time of the run be x, then the time of the bicycle race is 7-x (remember we are given that the total race time is 7 hours)

 

Total distance = 113 mi (we are given)

which is composed of the distances covered in the run and the bicycle race. So all we need to do is write them algebraically and equate to the total distance

We know that distance, d = time*velocity. So we can write

run distance = 7*x and bicycle race distance = 23*(7-x)

the sum of these two distances equals 113 mi

7x+23*(7-x)=113

7x+161-23x=113

x = 3 hours the time of the run

7-3=4 hrs the time of the bicycle race

run dist= 3*7 = 21 mi

bicycle dist = 113-21 = 92 mi