Question

Explain why if a runner completes a 6.26.2​-mi race in 3434 ​min, then he must have been running at exactly 1010 ​mi/hr at least twice in the race. Assume the​ runner's speed at the finish line is zero.

Answer 1

Answer:

All speed from 0 mi/h and 11 mi/h were reached because the initial and final speed was 0 mi/h the speed of 10 mi/hr was reached at least twice in the race.

Step-by-step explanation:

Given,

Total distance covered = 6.2 miles,

Time taken = 34 minutes = $\frac{34}{60}$ hours

( 1 hour = 60 minutes )

Since,

$Speed = \frac{Distance}{Time}$

Thus, the speed of the runner = $\frac{6.2}{\frac{34}{60}}$

$=\frac{6.2\times 60}{34}$

$=\frac{372}{34}$

= 10.9411764706

≈ 11 miles per hour

Thus, the average speed of the runner is 11 miles per hour ( approx )

By MVT,

The speed was exactly 10 mi/hr at least twice in the race.

By intermediate value theorem,

All speed from 0 mi/h and 11 mi/h were reached because the initial and final speed was 0 mi/h the speed of 10 mi/hr was reached at least twice in the race.