Question

Tim and Rick both can run at speed vr and walk at speed vw, with vr>vw. They set off together on a journey of distance D. Rick walks half of the distance and runs the other half. Tim walks half of the time and runs the other half.

Answer 1

Question:

How long does it take Rick to cover the distance D?

Answer:

The time, $t_R$, Rick takes to cover the distance D is;

$t_R = \frac{D}{2\times v_w} + \frac{D}{2\times v_r}$

Explanation:

Here we have the running speed of Rick = $v_r$ and

The walking speed of Rick = $v_w$

Therefore, since Rick walks half of the distance and runs the other half, we have

$Velocity = \frac{Distance }{Time} \\\\\therefore Time = \frac{Distance }{Velocity }$

Where

Distance for walking = D/2 and distance for running = D/2

Rick's time in running is

$t_{Rr} = \frac{D/2}{v_r}$ and time in walking is

$t_{Rw} = \frac{D/2}{v_w}$

Total time is given by

$t_{R} = \frac{D/2}{v_w} + \frac{D/2}{v_r}= \frac{D}{2\times v_w} + \frac{D}{2\times v_r}$