Required Mathematical Intelligence

Chapter 96

A fisherman, wearing a big straw hat, was fishing in a river in a rowboat.The river was flowing at three miles an hour, and his rowboat was traveling downstream at the same speed. "I've got to paddle some miles upriver," he said to himself, "the fish don't want to take the bait here!"

Just as he was beginning to row upstream a gust of wind blew his straw hat into the water beside the boat.However, our fisherman did not notice that he had lost his straw hat and continued to row upstream.He didn't realize this until he was rowing to a distance of five miles between the boat and the straw hat.So he immediately turned the bow of the boat, rowed downstream, and finally caught up with his straw hat floating in the water.

In still water, a fisherman always paddles at 5 miles an hour.He keeps this speed constant as he strokes upstream or downstream.Of course, this is not his speed relative to the bank.For example, when he paddles upstream at 5 miles an hour, the river will drag him downstream at 3 miles an hour, so that his speed relative to the bank is only 2 miles an hour; When paddling downstream, his rowing speed and the speed of the river's flow will combine to give him a speed of 8 miles per hour relative to the river bank.

If the fisherman lost his straw hat at 2:[-] p.m., when did he get it back?
[Answer: Since the speed of the river water has the same effect on the rowboat and the straw hat, the speed of the river water can be completely ignored when solving this puzzle.Although the water is flowing and the banks remain stationary, we can imagine the water being completely still and the banks moving.As far as rowboats and straw hats are concerned, this assumption is indistinguishable from the above.

Since the fisherman rowed 5 miles away from the straw hat, of course he rowed back 5 miles back to the straw hat.So, relative to the river, he rowed a total of 10 miles.The fisherman was paddling at 5 miles per hour relative to the water, so he must have spent a total of 2 hours paddling the 10 miles.So, at 4:[-] p.m., he retrieved his straw hat that had fallen into the water.

The situation is similar to that of calculating the speed and distance of objects on the Earth's surface.Although the earth rotates through space, this motion has the same effect on all objects on its surface, so for most problems of speed and distance, this motion of the earth can be completely ignored. ]
(End of this chapter)