The cat and dog race

Question

A dog and a cat race to a post 100 feet away and back, 200 feet in all. The dog covers 3 feet with each leap; the cat covers 2 feet with each leap; but the cat makes three leaps in the time the dog makes two. Each animal must reach or pass the post before turning, and turns take no time. Who wins the race?

Accepted Answer

The cat wins. Speeds are equal. In the time the dog makes 2 leaps of 3 feet (6 feet), the cat makes 3 leaps of 2 feet (6 feet). Same speed, so the race would be a dead heat if it were a straight run. The turn. The post is 100 feet away. The dog leaps 3 feet at a time: after 33 leaps it has covered 99 feet and must make a 34th leap to reach and pass the post, landing at 102 feet. It then needs 34 leaps back (102 feet, passing the start). Total 68 leaps. The cat leaps 2 feet at a time: exactly 50 leaps out to land precisely on the post, and 50 back: 100 leaps. Compare times. Measure time in uni…

The cat and dog race

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