start time of boat race

pysics help two boats start together….?

Two boats start together and race across a 58 km wide lake and back. Boat A goes across at 58 km/h and returns at 58 km/h. Boat B goes across at 29 km/h, and its crew, realizing how far behind it is getting, returns at 87 km/h. Turnaround times are negligible, and the boat that completes the round-trip first wins.
(a) Which boat wins? (Or is it a tie?) By how much?
(b) What is the average velocity of the winning boat?

Remember speed = distance divided by time, v = d/t. This can be rearranged to t = d/v, time is distance divided by speed.

Boat A crosses the lake in (58 km)/(58 km/h) = 1h to cross the lake and returns in (58 km)/(58 km/h) = 1 hr, so it finishes in 2 hours.

Boat B crosses the lake in (58 km)/(29 km/h) = 2 hours. So by the time it gets to the turn around Boat A is already crossing the finish line! But it returns in (58 km)/(87 km/h) = 0.6666 hours (= 40 minutes). So it finishes in 2 hours 40 minutes, meaning Boat A wins by 40 minutes.

b/. This is a trick question, the answer is 0. There is a subtle difference between speed and velocity. Speed is the distance travelled divided by time, so the winning boat, Boat A, travels an average speed of 58 km/h (which must be the case since it travelled the same speed both ways). But velocity is the displacement divided by time and since the winning boat finishes where it starts, the displacement is 0 km, which means the average velocity must be 0 km/h.

Roslagsloppet 2010 Tomta brygga, part 1. Swedish power boat racing.

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