Two Boats on a River
This problem is from Joe Black, Athens, Texas, by way of Marilyn vos Savant, Parade Magazine.
Two motorboats at opposite shores of a river start moving toward each other at constant, but different, speeds. (Neglect all other factors, like acceleration, turn-around and current.) When they pass each other the first time, they are 700 yards from one shoreline. They continue to the opposite shore, then turn around and start moving toward each other again. When they pass the second time, they are 300 yards from the opposite shoreline. How wide is the river?
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Solution to Two Boats on a River
Correct solutions: Wyatt Witemeyer
Let x be the unknown value of the width of the river. Here are some facts:
- When the boats meet the first time, the combined distance they have traveled must equal the width of the river.
- When the boats meet the second time, the combined distance they have traveled is three times the width of the river.
- Since the boats travel at constant (albeit different) rates, when they meet for the second time, each (separately) has traveled three times the distance they had traveled when they met the first time.
Therefore one boat has traveled 700*3 = 2100 yards. Since this boat is now 300 yards from the shore, the width of the river is
x = 2100 – 300 = 1800 yards.
