imc

Question

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?

Accepted Answer

Let x be the length of the ship. Then, in the time that Emily walks 210 steps, the ship moves 210-x steps. Also, in the time that Emily walks 42 steps, the ship moves x-42 steps. Since the ship and Emily have the same ratio of absolute speeds in either direction, 210210-x = 42x-42. Dividing both sides by 42 and cross multiplying, we get 5(x-42) = 210-x, so 6x = 420, and x = 70.