2021 AMC 12A Fall Problem 5

Question

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?

6

8

10

11

15

From the first pole to the

41

st pole there are

40

gaps, so each gap is

\dfrac{5280}{40}

feet

Elmer’s stride is one gap divided by

44;

Oscar’s leap is one gap divided by

12

There are

40

gaps between the first and

41

st poles, so each gap is

\dfrac{5280}{40} = 132

feet.

Elmer’s stride is

\dfrac{132}{44} = 3

feet and Oscar’s leap is

\dfrac{132}{12} = 11

feet, a difference of

11 - 3 = 8

feet.

Thus, the correct answer is B.

Problem 5 in other years