2021 AMC 10A Problem 6

Problem 6 of 25EasierAlgebra

Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking at

4

miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to

2

miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at

3

miles per hour. She meets Jean at the halfway point. What was Jean’s average speed, in miles per hour, until they meet?

Show solution

Solution

Let

2d

be the distance from the trailhead to the fire tower, where

d > 0.

Then Chantal hiked for

\dfrac{d}{4} + \dfrac{d}{2} + \dfrac{d}{3} = \dfrac{13d}{12}

hours. If Jean travelled

d

miles in

\dfrac{13d}{12}

hours, then his speed was

d \div \dfrac{13d}{12} = \dfrac{12}{13}

miles per hour. Thus, A is the correct answer.