Traveling along a river, a man in a row boat loses his hat when he passes under a bridge, but he keeps going in the same direction. In 15 minutes, he realizes that he lost his hat, and rows his boat the other way until he is able to retrieve his hat 1 km away from the bridge. What is the speed of the river's current?

Step-by-step explanation:

Let the speed of the boat in still water is x km per minute and the water is r  km per minute.

The speed of the boat in downstream is (x + r) km per minute and in upstream is (x - r) km per minute.

First, the man was moving in upstream, because the hat was retrieved 1 km away from the bridge.

After losing the hat the man traveled 15 minutes upstream, hence he went 15(x - r) km far from the bridge.

After 15 minutes he was coming back to collect his hats.

Let, he has traveled downstream for t minutes to get his hat.

Hence, t(x + r) = 15r + tr +  15(x - r) or, tx = 15x or, t = 15.

Again, 15r + 15r = 1 km or, r = km = meters.