Question

Suppose you have entered an 81​-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 30 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

Distance of the run = 21 miles

Distance of bicycle race = 60 miles

Explanation:

Distance = average velocity × time

Let the time and distance of the run, respectively, be
`t_1` and
`d_1`.

Let those of the bicycle race be
`t_2` and
`d_2`.

From the question,

`t_1+t_2=5`

`d_1=7t_1` and
`d_2=30t_2`

Total distance = 81

`d_1+d_2=81`

`7t_1+30t_2=81`

Solving the two equations involving
`t_1` and
`t_2`, we have

`t_1=3` and
`t_2=2`

`d_1=7t_1=7*3=21` and

`d_2=30t_2=30*2=60`

Hence, the distance of the run,
`t_1` is 21 miles

Distance of bicycle race,
`d_2` is 60 miles.