A medium question on meeting for P4–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 boy leaves home and walks to the library at 50 m a minute.
10 minutes later his older brother leaves home and cycles after him along the same road at 150 m a minute.
He catches up before the boy reaches the library.
How many minutes after setting off does the older brother catch up?
Show the hints (2)
💡Hint 1: When the older brother sets off, how far ahead is the boy already?
💡Hint 2: After that, how much more does the older brother cover each minute?
Worked solution
Have a go first, then read the solution step by step.
1.When his brother sets off, the boy has walked for 10 minutes: 50 × 10 = 500 m.
2.Then each minute the older brother rides 150 m and the boy walks 50 m: the gap closes by 150 − 50 = 100 m.
3.A 500 m gap closing by 100 m a minute: 500 ÷ 100 = 5, so he catches up 5 minutes after setting off.
⚠️Common mistake: 5 + 10 = 15 minutes counts from when the boy left; the question asks from when his brother set off.
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