Two boats start at the same time from opposite sides of a river, travelling at right angles to the shores at a constant speed. First time, they pass each other at a point 72 m from the nearer shore. Both boats rest for 30 minutes at their respective shores before starting back. In the return trip, they meet at 40 m from the other shore. Find the width of the river.

Let the speeds of the two boats be v1 and v2, and let the width of the river be W. At their first meeting, the combined distance traveled by both boats is W, so the ratio of their distances is 72 divided by (W minus 72). At their second meeting, the combined distance traveled is 3W; the first boat traveled (W plus 40) and the second traveled (2W minus 40). Setting the ratios equal gives 72 divided by (W minus 72) equals (W plus 40) divided by (2W minus 40). Solving the equation 144W minus 2880 equals W squared minus 32W minus 2880 yields W equals 176. The result is 176 m.

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