A boat 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 and 40u + 55d = 13.

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

Then 30u = 10 − 4 = 6, so u = 1/5 → upstream speed = 5 km/h.

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

Tip: Substituting reciprocals converts time equations into linear ones.