Numerical answer
A boat covers 30 km upstream and 44 km downstream in 10 hours. It covers 40 km upstream and 55 km downstream in 13 hours. What is the speed of the boat in still water, in km/h?
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Answer: 8
Let u = 1/(upstream speed) and d = 1/(downstream speed).
30u + 44d = 10 … (i)
40u + 55d = 13 … (ii)
(i) × 4: 120u + 176d = 40; (ii) × 3: 120u + 165d = 39. Subtracting: 11d = 1 ⇒ d = 1/11, so the downstream speed is 11 km/h.
From (i): 30u = 10 − 4 = 6 ⇒ u = 1/5, so the upstream speed is 5 km/h.
Still-water speed = (11 + 5)/2 = 8 km/h (the stream flows at 3 km/h).
30u + 44d = 10 … (i)
40u + 55d = 13 … (ii)
(i) × 4: 120u + 176d = 40; (ii) × 3: 120u + 165d = 39. Subtracting: 11d = 1 ⇒ d = 1/11, so the downstream speed is 11 km/h.
From (i): 30u = 10 − 4 = 6 ⇒ u = 1/5, so the upstream speed is 5 km/h.
Still-water speed = (11 + 5)/2 = 8 km/h (the stream flows at 3 km/h).
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