Problem:
Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts 210 equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts 42 steps of the same size from the front of the ship to the back. In terms of Emily's equal steps, what is the length of the ship?
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Solution:
Let denote the required length of the ship. Assume Emily's speed is 1 and let denote the speed of the ship relative to the riverbank. When Emily walks from the back to the front, it takes 210 steps, so . Similarly, when Emily walks from the front to the back of the ship, it takes 42 steps, so . Solving this system yields and .
The problems on this page are the property of the MAA's American Mathematics Competitions