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 = (D)/(2* v_w) + (D)/(2* v_r)`

Step-by-step 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 = (Distance )/(Time) \\\\\therefore Time = (Distance )/(Velocity )`

Where

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

Rick's time in running is

`t_(Rr) = (D/2)/(v_r)` and time in walking is

`t_(Rw) = (D/2)/(v_w)`

Total time is given by

`t_(R) = (D/2)/(v_w) + (D/2)/(v_r)= (D)/(2* v_w) + (D)/(2* v_r)`