A motorboat travels 30 km upstream and 44 km downstream in 10 hours. It travels 40 km upstream and 55 km downstream in 13 hours.

Let u = 1/(upstream speed) and d = 1/(downstream speed).

30u + 44d = 10 … (1)
40u + 55d = 13 … (2)

Multiply (1) by 4 and (2) by 3: 120u + 176d = 40 and 120u + 165d = 39. Subtracting, 11d = 1 → d = 1/11, so downstream speed = 11 km/h.

From (1): 30u = 10 − 4 = 6 → u = 1/5, upstream speed = 5 km/h.

Boat speed = (11 + 5)/2 = 8 km/h (stream = 3 km/h).

Check: 30/5 + 44/11 = 6 + 4 = 10 ✓; 40/5 + 55/11 = 8 + 5 = 13 ✓.