Two boats on opposite sides of a river head towards each other at different speeds. When they pass each other the first time they are 700 yards from one shoreline. They continue to the opposite shoreline, turn around, and move towards each other again. When they pass the second time they are 300 yards from the other shoreline.
How wide is the river? (Assume both boats travel at a constant speed and ignore factors such as turn-around time and the current of the river).
Silverknight, thanks for your comments. I stand by my conclusion that we do not need to calculate the speed of either boat to determine the river width. We do know that one boat has traveled 700 yards at the first meeting, at which time the combined distance traveled by both boats is equal to the river width. We also know that both boats proceed to their respective far shores and then are in the process of returning to their home shores when they meet again. At this second meeting, the combined distance traveled by both boats is equal to three x the river width. Since the problem states that both boats travel at constant speed, the selected boat has traveled 700 yards x 3 = 2,100 yards. Since the problem states the boat at this time is returning to the shore from which it departed and is some 300 yards from the opposite shore, the width of the river must be 2,100 - 300 = 1,800 yards. Gordon S.
In Defense of Limited Equations
