Problem:
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 miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they meet?
Answer Choices:
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Solution:
Recall that distance equals rate times time, so time equals distance divided by rate. Let denote the distance to the fire tower, in miles. The elapsed time, in hours, in the period described is for Chantal to reach the halfway point, plus for her to hike from the halfway point to the tower, plus for her to hike back from the tower to the halfway point. The total time elapsed is . Because Jean hikes distance in this time, her rate is .
The problems on this page are the property of the MAA's American Mathematics Competitions