Olympiad topic · P5–P6
Boats and currents
Boats going with and against the current appear in the Hua Xia Cup's P5 and P6 first rounds, qualifying rounds and finals.
Try one
★★ MediumA 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?
- 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.
- 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.
Answer: 4 hours
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsStraight downstream or upstream.
- ★★MediumFree2 question types · unlimited questionsBoat or current speed from the times there and back.
- ★★★HardFree4 question types · unlimited questionsA lifebuoy dropped, a faster current.
- ★★★★Expert (competition level)VIP3 question types · unlimited questionsThe average speed there and back, two boats and a float together.
Boats and currents: what it is and how to solve it
A boat going downstream or upstream: the current speeds it up or slows it down.
For example: A boat does 20 km/h in still water; the river flows at 3 km/h. 92 km downstream takes? 20 + 3 = 23 km/h, 92 ÷ 23 = 4 hours.
The key idea: Downstream speed = boat + current, upstream = boat − current. So boat speed = (down + up) ÷ 2 and current = (down − up) ÷ 2.
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