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

Answer:

Distance of the run = 21 miles

Distance of bicycle race = 60 miles

Step-by-step 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 $t_2=2$

$d_1=7t_1=7\times3=21$ and

$d_2=30t_2=30\times2=60$

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

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