Numerical answer
A boat covers 18 km upstream and 50 km downstream in 8 hours. It covers 30 km upstream and 25 km downstream in 7.5 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).
18u + 50d = 8 and 30u + 25d = 7.5.
Multiply the second equation by 2: 60u + 50d = 15. Subtract the first: 42u = 7 → u = 1/6, so upstream speed = 6 km/h.
Substitute back: 30(1/6) + 25d = 7.5 → 5 + 25d = 7.5 → d = 1/10, so downstream speed = 10 km/h.
Boat speed in still water = (6 + 10)/2 = 8 km/h (stream speed = 2 km/h).
18u + 50d = 8 and 30u + 25d = 7.5.
Multiply the second equation by 2: 60u + 50d = 15. Subtract the first: 42u = 7 → u = 1/6, so upstream speed = 6 km/h.
Substitute back: 30(1/6) + 25d = 7.5 → 5 + 25d = 7.5 → d = 1/10, so downstream speed = 10 km/h.
Boat speed in still water = (6 + 10)/2 = 8 km/h (stream speed = 2 km/h).
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