Question

A summer biathalon-style race requires running a certain distance, and then biking a distance 2 miles more than the length of the run. One athlete has a running speed of 6 miles per hour, and a biking speed of 10 miles per hour, and completes the event in 90 minutes. How long, in miles, is each segment of the race

Answer 1

The run is 4.875 miles long, while, the bike is 6.875 miles long.

Explanation:

Let d = running distance and d' = biking distance.

Given that d' = d + 2 and v = running speed = 6 mph and v' = biking speed = 10 mph.

Since time, t = distance/speed, running time, t = running distance/running speed = d/6 and biking time, t' = biking distance/biking time = d'/10 = (d + 2)/10.

Since the total time, t" = 90 minutes = 1.5 hours,

t + t' = t"

So, d/6 + (d + 2)/10 = 1.5

multiplying through by the L.C.M, 30, we have

30 × d/6 + 30 ×(d + 2)/10 = 30 × 1.5

5d + 3(d + 2) = 45

expanding the brackets, we have

5d + 3d + 6 = 45

collecting like terms, we have

8d = 45 - 6

8d = 39

d = 39/8

d = 4.875 miles

d' = d + 2 = 4.875 + 2 = 6.875 miles

So, the run is 4.875 miles long, while, the bike is 6.875 miles long.