2021 Fall AMC 10A Problem 6

Elmer the emu takes

44

equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in

12

equal leaps. The telephone poles are evenly spaced, and the

41

st pole along this road is exactly one mile (

5280

feet) from the first pole. How much longer, in feet, is Oscar’s leap than Elmer’s stride?

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Solution

There are

40

gaps between the

1

st and

41

st pole, which means that the distance between consecutive poles is

5280 \div 40 = 132

feet. This means that each of Elmer’s strides is

132 \div 44 = 3

feet. Similarly, each of Oscar’s leaps is

132 \div 12 = 11

feet. This makes Oscar’s leap

11 - 3 = 8

feet longer. Thus, B is the correct answer.