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
Piers A and B stand on a river 144 km apart, A upstream and B downstream.
A speedboat sets off downstream from A towards B, and at the same moment a cargo boat sets off upstream from B towards A.
In still water the speedboat does 24 km an hour and the cargo boat 12; the river flows at 2 km an hour.
All three speeds stay the same.
How far from pier A do the two boats meet?
Show the hints (3)
💡Hint 1: How far does each boat really go in an hour, and how much closer do they get each hour?
💡Hint 2: They close (24 + 2) + (12 − 2) km an hour. Does the current change when they meet?
💡Hint 3: They meet after 4 hours. How fast was the speedboat really going all that time?
Worked solution
Have a go first, then read the solution step by step.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download