Monday, October 18, 2004

Width of the River

Two ferry boats start at the same instant on opposite sides of the river. One is faster than the other. They cross at a point 720 yards from the left shore on their way to their respective destinations, where each one spends 10 minutes to change passengers before the return trip. They meet again at a point 400 yards from the right shore. How wide is the river?

Answer:

The above problem was first published by Sam Lloyd, an American and the greatest puzzlist ever lived, has this following ingenious solution to offer:

The first time the boats meet, they have travelled a combined length equal to the width of the river. The second time, they have travelled a combined length equal to three times the river's width. The boat which had travelled 720 yd at the first meeting has therefore travelled three times that (2160 yd) at the second meeting. As this boat has then travelled the width of the river plus 400 yd, the river is thus shown to be 1760 yd wide.