Tim and Rick both can run at speed v_r and walk at speed v_w, with v_r > v_w 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. How long does it take Rick to cover the distance D? Express the time taken by Rick in terms of v_r, v_w, and D.

The time taken by Rick is Δt = (D/2 / v_w) + (D/2 / v_r)

Explanation:

Hi there!

The equation of average velocity (v) is the following:

v = Δx / Δt

Where:

Δx = traveled distance.

Δt = elapsed time.

During the first half of Rick's journey, the average velocity can be written as follows:

v_w = D/2 / Δt1

Solving for Δt1:

Δt1 = D/2 / v_w

For the second half of the trip:

v_r = D/2 / Δt2

Δt2 = D/2 / v_r

The time it takes Rick to cover the distance D will be equal to Δt1 + Δt2

Δt = Δt1 + Δt12

Δt = (D/2 / v_w) + (D/2 / v_r)

The time taken by Rick is Δt = (D/2 / v_w) + (D/2 / v_r)