The boat passed 2 hours upstream and 3 hours downstream. During this time, it covered 88 km.

The boat passed 2 hours upstream and 3 hours downstream. During this time, it covered 88 km. Find the current speed and the speed of the boat in still water if it has traveled 32 km more downstream than against the current.

Let the boat’s own speed be equal to x km / h, and the current speed is equal to y km / h. The speed of the boat along the river is (x + y) km / h, and the speed of the boat against the river is (x – y) km / h. The boat covered (3 (x + y) + 2 (x – y)) kilometers or 88 km in 3 hours downstream and 2 hours upstream. It is also known that in 3 hours downstream the boat covered a greater distance than in 2 hours against the current for (3 (x + y) – 2 (x – y)) kilometers or 32 km. Let’s compose a system of equations and solve it.

3 (x + y) + 2 (x – y) = 88; 3 (x + y) – 2 (x – y) = 32;

3x + 3y + 2x – 2y = 88; 3x + 3y – 2x + 2y = 32;

5x + y = 88; x + 5y = 32;

x = 32 – 5y;

5 (32 – 5y) + y = 88;

160 – 25y + y = 88;

-24y = 88 – 160;

-24y = – 72;

y = -72: (-24);

y = 3 (km / h) – current speed;

x = 32 – 5y = 32 – 5 * 3 = 32 – 15 = 17 (km / h) – own speed of the boat.

Answer. The speed of the boat is 17 km / h, the speed of the current is 3 km / h.