Numerical answer
A boat goes 30 km upstream and 44 km downstream in 10 hours. It goes 40 km upstream and 55 km downstream in 13 hours. What is the speed of the stream (in km/h)?
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Answer: 3
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, so d = 1/11 and the downstream speed is 11 km/h.
From (i): 30u = 10 − 4 = 6, so u = 1/5 and the upstream speed is 5 km/h.
Stream speed = (11 − 5)/2 = 3 km/h (boat speed 8 km/h).
Tip: Use reciprocals of the speeds as the unknowns so the time equations become linear.
30u + 44d = 10 …(i)
40u + 55d = 13 …(ii)
(i) × 4: 120u + 176d = 40; (ii) × 3: 120u + 165d = 39. Subtracting: 11d = 1, so d = 1/11 and the downstream speed is 11 km/h.
From (i): 30u = 10 − 4 = 6, so u = 1/5 and the upstream speed is 5 km/h.
Stream speed = (11 − 5)/2 = 3 km/h (boat speed 8 km/h).
Tip: Use reciprocals of the speeds as the unknowns so the time equations become linear.
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