A hard question on boats and currents for 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 small ferry runs between piers A and B on a river, 480 m apart, with A upstream.
Usually it takes 4 minutes downstream from A to B and 6 minutes back upstream.
One day, after heavy rain, the river runs faster: the trip downstream from A to B takes only 3 minutes.
The ferry's still-water speed never changes, and that day's current stays steady.
That day, how many minutes does the trip back upstream from B to A take?
Show the hints (3)
💡Hint 1: First find the usual downstream and upstream speeds, and the downstream speed after the rain.
💡Hint 2: How much faster is the downstream speed after the rain? The ferry hasn't changed, so that is how much faster the current is.
💡Hint 3: The current is 40 m a minute faster. Upstream, that comes off the usual upstream speed of 80 m a minute.
Worked solution
Have a go first, then read the solution step by step.
1.Usually: downstream 480 ÷ 4 = 120 m a minute, upstream 480 ÷ 6 = 80 m a minute.
2.After the rain, downstream: 480 ÷ 3 = 160 m a minute, 160 − 120 = 40 more than usual, so the current is 40 m a minute faster.
3.Upstream after the rain: 80 − 40 = 40 m a minute.
4.480 ÷ 40 = 12 minutes.
⚠️Common mistake: thinking the upstream trip also gets quicker, or that it takes 1 more minute just as downstream took 1 fewer. A faster current only slows the upstream trip, and not by the same time.
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