Who is asking: Student
On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.
How fast is the river flowing?
Hints: This problem involves relative velocities. You can do it without any equations; you need only make two calculations.
The problem is to see the relationship between the hat and the boat taking place on the river with no reference to the shore. One way to do this is to imagine that the river is stationary and the shore is moving. From this vantage point the hat stays stationary in the river and you row away for ten miniues, and hence to return to it you need to row back towards the hat for ten minutes.
Someone on the shore has notices that the hat (or the shore) has moved one mile in this time so the river is flowing at one mile in twenty minutes, or 3 miles per hour.
I find this easier to see if I imagine that it takes place on a people mover like you see in airports rather than on a river. If you walk "the wrong way" on this moving belt, drop your hat and continue to walk for 10 steps, then turning around to retrieve your hat you have to return 10 steps.
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