A motorboat takes 10 hours to travel 40 km upstream and 60 km downstream. It takes 11 hours to travel 32 km upstream and 84 km downstream.

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

40u + 60d = 10 … (i)
32u + 84d = 11 … (ii)

Multiply (i) by 4 and (ii) by 5: 160u + 240d = 40 and 160u + 420d = 55. Subtracting: 180d = 15 ⇒ d = 1/12, so downstream speed = 12 km/h.

Then 40u = 10 − 5 = 5 ⇒ u = 1/8, upstream speed = 8 km/h.

Boat speed = (12 + 8)/2 = 10 km/h; stream speed = (12 − 8)/2 = 2 km/h.

Tip: Treat reciprocals of speeds as the unknowns — the equations become linear.