The speed of a motor boat when moving in the lake is 2 km / h more than its speed when moving against the stream of the river.

The speed of a motor boat when moving in the lake is 2 km / h more than its speed when moving against the stream of the river. Find the speed of the boat if, in 3 hours while moving along the river and 2 hours against the current, the boat has covered distances that differ by 22 km from each other.

We take the boat’s own speed as x (it coincides with the speed in the lake), then:
x + 2 – boat speed along the river;
x – 2 – upstream speed;
3 * (x + 2) – distance in 3 hours downstream;
2 * (x – 2) – 2 hours distance upstream.
Since the distance difference is 22 km, we get the equation:
3 * (x + 2) – 2 (x – 2) = 22;
3x + 6 – 2x + 4 = 22;
x = 22 – 10;
x = 12.
Answer: the required boat speed is 12 km / h.