Two ferries
Two ferries leave opposite shores of a river at the same moment, each at its own constant speed. They first pass each other 720 yards from the shore that the first ferry left. Each turns around instantly at the far shore, and they pass again 400 yards from the other shore (the one the first ferry sailed to).
How wide is the river, in yards?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
At the first meeting, the two ferries together have covered one width of the river. How much at the second meeting?
Each ferry covers the same fraction of the combined distance throughout, since their speeds are constant.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. At the first meeting the two ferries have together covered one river width; at the second, three widths. With constant speeds, each ferry's share of the combined distance is fixed, so the first ferry has gone three times as far at the second meeting as at the first.
Step 1: first meeting. Together they have covered one width , and the first ferry has done 720 yards of it.
Step 2: second meeting. By then, each has crossed the river once and started back, so together they have covered . The first ferry has gone yards.
Step 3. The first ferry has crossed the whole river and come back 400 yards: , so exactly one mile.
Read carefully. If the 400 yards were measured from the shore the first ferry started from, the same argument would give and . The statement fixes which shore is meant.