Question

A runner ran V1 km/hr for the first half of the race. The runner then ran V2 km/h for the second half of the race. What was the average speed of this runner? It is okay for the answer to be in variables.

Answer 1

Answer:

$v=\frac{v_{1}v_{2}}{\left ( v_{1}+v_{2} \right )}$

Explanation:

Let the distance traveled in first half is d and then in the next half is also d.

Let the time taken in first half is t1 and the time taken  in the second half is t2.

$t_{1}=\frac{d}{v_{1}}$

$t_{2}=\frac{d}{v_{2}}$

Total time taken

$t=t_{1}+t_{2}=\frac{d}{v_{1}}+\frac{d}{v_{2}}=\frac{d\left ( v_{1}+v_{2} \right )}{v_{1}v_{2}}$

The average speed of a body is defined as the total distance traveled by teh body to the total time taken.

$Average speed = \frac{total distance}{total time}$

$v=\frac{2d}{t}$

$v=\frac{2d}{\frac{2d\left ( v_{1}+v_{2} \right )}{v_{1}v_{2}}}$

$v=\frac{v_{1}v_{2}}{\left ( v_{1}+v_{2} \right )}$