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Play With These Old "Rate" Classics

Many problems are repeated to the point that they become classics. Below are three such classics involving rates, possibly in new clothes.

[#1] A water lily on a lake doubles in size each day. In one month it will cover the entire lake. How long would it take two such lilies to cover the lake?

[#2] Two runners, heading towards each other at five mph on a straight road, are ten miles apart. A fly, moving at 40 mph, leaves from the first runner , flies straight to the second runner, turns around, and flies straight back to the first runner...repeating this process continually. When the two runners meet, how far will the fly have flown?

[#3] Two cars depart at the same time. The first takes a minute to go around the course, while the second takes a minute and five seconds. After how many laps will the second car catch up to the first car?


Source: J. Baillif's "Let's Cere-brate," Reader's Digest, 1982, p. 27

Hint: Stop...Think...before you start cranking out equations involving rates (e.g. d = rt).


Solution Commentary: Author Baillif offered these responses as solutions...do you agree with him?

[#1] On day 2, one lily would equal two lilies. Thus, for two lilies to cover the lake from the start, it takes one month less one day.

[#2] As the two runners met at the end of an hour, the fly will have flown 40 miles.

[#3] The second car will never catch up, as the first car is going faster.