Answer to September 2003 Newsletter Brain Teaser:

The beauty of this month's brainteaser is that you don't need to know anything about the boats' relative speeds to figure out the width of the river (although you can certainly deduce the relative speeds after obtaining the answer).

When the boats first meet, the total distance they have traveled equals the width of the river. By the time they meet again, the total distance traveled equals three times the width of the river. (Draw a diagram to convince yourself.) The boats are each traveling at a constant speed, so they each will have traveled three times as far by the second meeting as the distance they'd traveled by the first time they met.

Because the boat starting in New York had traveled 720 yards at the first meeting, it must have traveled 2,160 yards at the time of the second meeting. But this distance is 400 yards from the other shore, so the width of the river equals 2,160 - 400 = 1,760 yards. Conveniently, this is exactly one mile.