Two bicyclists were 30 miles apart on a straight desert road. At the same moment that one bicyclist started pedaling towards the other at 8 mph, the second bicyclist started pedaling towards the first at 7 mph.

On a dare from a friend, a hummingbird started on the helmet of the first bicyclist. When the bicyclist started riding, the hummingbird took off and headed straight for the second bicyclist at 40 mph. He flew until he was able to touch the helmet of the second bicyclist. He turned around immediately and headed for the helmet of the first bicyclist. He continued like this—flying back and forth between the cyclists—until the two met somewhere along the road and had lunch.

How far will the hummingbird fly during the time the cyclists are riding?

Solution

I like this problem because no complicated math is involved, even though many people–especially math teachers—will think that complex math is required. In fact, you can do this problem in your head.

The closing speed of the two cyclists is 15 mph. That means that they'll meet for lunch along the road in two hours. Ignoring the seconds the bird requires to turn around each time he touches a helmet, he'll fly about 80 miles.

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