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Question

A power boat and a raft both left dock A on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock B downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock A. How many hours did it take the power boat to go from A to B?

Accepted Answer

WLOG let the speed of the river be 0. This is allowed because the problem never states that the speed of the current has to have a magnitude greater than 0. In this case, when the powerboat travels from A to B, the raft remains at A. Thus the trip from A to B takes the same time as the trip from B to the raft. Since these times are equal and sum to 9 hours, the trip from A to B must take half this time, or 4.5 hours. The answer is thus 4.5. Remark: This is equivalent to viewing the problem from the raft's perspective.