In detail

The ferry problem

The ferry problem

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The following enigma was proposed by the fantastic Sam Loyd in his puzzle encyclopedia.

Two ships depart from the opposite banks of a river at the same time and are located 720 yards from the port. Once they reach the opposite end of the river, they make a 10-minute stop and on the return trip they are 400 yards from the other port.

What is the width of the river?


Although there is a mathematical solution to the problem, it is possible to solve it by applying only logic. Look at the image shown below in which the two meetings of the ships are reproduced.

The first encounter tells us that it takes place 720 yards from the first port. At that time, the total distance traveled by the two ships corresponds to the width of the river, as shown in the drawing. Once they reach their destination, the total distance traveled by both ships is twice the width of the river. The time they spend in port does not affect the solution.
In their second meeting, the total distance traveled by both ships is three times the width of the river. It is obvious then that each ship has traveled three times the distance at which its first encounter took place. Then the ship "A" has traveled 720 x 3 = 2160 Yards. Since we know that it is 400 yards from the second port, we can deduce that the river is 2160-400 wide = 1760 yards (1 mile).