A hard question on meeting for P5, with a step-by-step solution, diagrams and the answer. The basis of journey problems: meeting and catching up appear in the Hua Xia Cup's P4 to P6 qualifying rounds and finals.
The question
A hiking trail joins village A and village B.
Ka-lok walks from A towards B and Tsz-ching from B towards A, setting off at the same moment and keeping steady speeds.
Ka-lok walks 12 m a minute faster than Tsz-ching.
They meet 10 minutes after setting off.
After the meeting, Ka-lok walks another 8 minutes and reaches village B.
How far apart are the two villages, in metres?
Show the hints (3)
💡Hint 1: The stretch Ka-lok walks after the meeting — who walked it before the meeting?
💡Hint 2: Tsz-ching took 10 minutes over that stretch; Ka-lok takes only 8. How do their speeds compare?
💡Hint 3: Their speeds are Ka-lok : Tsz-ching = 10 : 8 = 5 : 4; the difference of 1 part is 12 m. So Ka-lok walks 60 m a minute and Tsz-ching 48 m.
Worked solution
Have a go first, then read the solution step by step.
1.After the meeting Ka-lok covers exactly the stretch Tsz-ching walked in 10 minutes — and he takes only 8.
2.Same stretch, less time, faster walker: Ka-lok : Tsz-ching = 10 : 8 = 5 : 4.
3.The difference, 5 − 4 = 1 part, is 12 m, so one part is 12 m: Ka-lok walks 60 m a minute, Tsz-ching 48 m.
4.Distance = both walks added = 60 × 10 + 48 × 10 = 600 + 480 = 1080 m.
⚠️Common mistake: writing the speed ratio the wrong way round as 4 : 5. Less time means faster.
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