The two ferries and the width of the river

Question

Two ferries start at the same instant from opposite banks of a river and cross at constant (but different) speeds along the same straight line. They first pass each other 720 metres from the nearer bank. Each continues to the far bank, waits 10 minutes, and starts back. On the return trips they pass each other 400 metres from the other bank.

How wide is the river? (This is one of Sam Loyd's puzzles; there is a way to do it with almost no algebra.)

Accepted Answer

1,760 metres. Count widths. When the ferries first meet, their combined distance travelled is exactly one river width W. At the second meeting, each ferry has crossed once and come partway back, so their combined distance is three river widths, 3W. (The 10-minute waits are equal for both, so they do not affect the comparison.) Use the ratio. Since both ferries run at constant speeds and have been travelling for the same time (minus equal waits), each ferry's share of the combined distance is the same at both meetings. Call the ferry that had covered 720 m at the first meeting ferry A. At the …

The two ferries and the width of the river

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