Problem:
A power boat and a raft both left dock 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 downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock . How many hours did it take the power boat to go from to ?
Answer Choices:
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Solution:
Assume the power boat and raft met at point on the river. Let be the speed of the boat and be the speed of the raft and the river current. Then is the speed of the power boat downstream and is the speed of the power boat upstream. Let the distance between the docks be , so that and . Then because time is equal to distance divided by rate,
Rearrange to find that . Then the time it took the power boat to go from to is
OR
In the reference frame of the raft, the boat simply went away, turned around, and came back, all at the same speed. Because the trip took 9 hours, the boat must have turned around after hours.
The problems on this page are the property of the MAA's American Mathematics Competitions