Question: 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.
Find Rick's average speed for covering the distance D. Express Rick's average speed in terms of v_r and v_w.
How long does it take Tim to cover the distance? Express the time taken by Tim in terms of v_r, v_w, and D.
Who covers the distance D more quickly?
In terms of given quantities, by what amount of time, Delta t, does Tim beat Rick? It will help you check your answer if you simplify it algebraically and check the special case v_r = v_w Express the difference in time, Delta t in terms of v_r, v_w, and D.
In the special case that v_r = v_w, what would be Tim's margin of victory Delta t(v_r = v_w)?