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 straight cycle track runs between two MTR stations, A and B.
Ka-lok sets off from A and Tsz-ching from B at the same moment, cycling towards each other.
Ka-lok rides 180 m a minute and Tsz-ching 130 m a minute.
When they meet, Ka-lok has ridden 250 m more than Tsz-ching.
How long is the cycle track?
Show the hints (3)
💡Hint 1: Each minute, how much further does Ka-lok ride than Tsz-ching?
💡Hint 2: From the 250 m difference you can tell how many minutes they rode.
💡Hint 3: They rode for 5 minutes before meeting; together they cover 180 + 130 m a minute.
Worked solution
Have a go first, then read the solution step by step.
1.Each minute Ka-lok rides 180 m and Tsz-ching 130 m: Ka-lok gains 180 − 130 = 50 m.
2.By the meeting Ka-lok has ridden 250 m more, gaining 50 m a minute: 250 ÷ 50 = 5, so they meet after 5 minutes.
3.Track = both rides added = 180 × 5 + 130 × 5 = 900 + 650 = 1550 m.
⚠️Common mistake: working out the time as 250 ÷ (180 + 130). The difference between their distances grows by only 50 m a minute.
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