A medium question on boats and currents for P5–P6, with a step-by-step solution, diagrams and the answer. Boats going with and against the current appear in the Hua Xia Cup's P5 and P6 first rounds, qualifying rounds and finals.
The question
A cargo boat goes 14 km an hour in still water, and the river flows at a steady speed.
It sails downstream from pier A to pier B, 48 km away, in 3 hours.
How many hours does the cargo boat take to go back upstream from B to A?
Show the hints (2)
💡Hint 1: The outward trip gives the downstream speed. How much faster than the boat's own speed is it?
💡Hint 2: That difference is the current. Upstream, take the current off the boat's speed.
Worked solution
Have a go first, then read the solution step by step.
1.Downstream speed: 48 ÷ 3 = 16 km/h.
2.Current: 16 − 14 = 2 km/h.
3.Upstream speed: 14 − 2 = 12 km/h.
4.48 ÷ 12 = 4 hours.
⚠️Common mistake: thinking the way back also takes 3 hours, or dividing by the boat's speed 14. Upstream is slower.
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