A boy was drifting downstream on a log in the Tisza. Three boats were moving upstream on the water, the first one's own speed was , the second one's was h, and the third one's was h. At a bridge pier, they all passed by the boy at the same time, but none of them noticed. An hour later, the crews of all three boats heard on the radio that a boy was on the log. All three immediately turned around to rescue the boy. The boy's parents learned in the evening that he was rescued from the water downstream from the bridge pier. Which boat was the rescuer?
Problem 889
Official solution
Let's denote the speed of the river current as . Then, the first boat traveled upstream at a speed of , and since it traveled for exactly 1 hour, the distance it covered was . Then it turned around, and to catch up with the child, it had to travel a distance of , and its speed was (since the current now helped).
We can write the following equation for the equality of times: . From this, we find that the speed of the river current is . Knowing this, it is easy to calculate that all three boats arrived at the same time to rescue the child.