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2021 AMC Fall 10A Problem 6

2021 AMC Fall 10A Problem 6AMC 10 Step by Step

Name: Date: September 13, 2026

Linear Equations & Word Problems · difficulty 2 of 5 · about 2 min · position P1-10

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?

A)
$6$
B)
$8$
C)
$10$
D)
$11$
E)
$15$

Answer

Key insight

There are 40 gaps, not 41, so each gap is 5280/40 = 132 feet; a stride is 132/44 = 3 feet and a leap 132/12 = 11 feet.

Solution

From the first pole to the $41$ st pole there are $41 - 1 = 40$ gaps, so consecutive poles are
$\frac{5280}{40} = 132 \text{ feet apart.}$

Elmer covers $132$ feet in $44$ strides, so one stride is $132 / 44 = 3$ feet. Oscar covers the same $132$ feet in $12$ leaps, so one leap is $132 / 12 = 11$ feet.

The leap exceeds the stride by $11 - 3 = 8$ feet.

The answer is $\boxed{\textbf{(B)}\ 8}$ .

Why this works

Everything is measured against one common length, the pole spacing, so find that first and then convert it into each animal's unit. The one subtlety is the fencepost count: $41$ poles enclose $40$ intervals. The fact that $5280/41$ is not an integer is a built-in sanity check.

The trap

Dividing the mile by 41 poles instead of 40 gaps between the first and forty-first pole.

Common mistakes

Dividing the mile by 41 poles instead of 40 gaps between the first and forty-first pole.
Answering $11$ (Oscar's leap) instead of the difference, or dividing the stride counts $44/12$ as if that were the ratio asked for.

Techniques

Set up the equation/formula and compute; no special trick needed