Question

Running and Walking Review Part A 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. How long does it take Rick to cover the distance D? Express the time taken by Rick in terms of vr, w, and D. View Available Hint(s) Submit Part B Find Rick's average speed for covering the distance D Express Rick's average speed in terms of vr and Uw View Available Hint(s) Vave R Submit

Answer 1

Part A -

As mentioned in the problem, Rick walks half the distance and runs the other half.

So, for Rick:

Vr*Tr = D/2

=> Tr = D / (2*Vr)----------------------------------------------(i)

and -

Vw*Tw = D/2

=> Tw = D / (2*Vw)--------------------------------------------(ii)

So, time taken by Rick to cover the total distance D, T = Tr + Tw

= D / (2*Vr) + D / (2*Vw)

   = (D/2)*(1/Vr + 1/Vw)

= (D/2)*[(Vw + Vr)/(Vr*Vw)]

Part - B -

Average velocity of Rick = D/T = D / [(D/2)*[(Vw + Vr)/(Vr*Vw)]] = 2*(Vr*Vw) / ((Vw + Vr)