An easy question on meeting for P3–P4, 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
Two brothers run the same way along a park running track.
At the start the younger is 8 m ahead of the older.
They set off together: the older runs 4 m a second, the younger 2 m a second.
After how many seconds does the older brother catch up?
Show the hints (2)
💡Hint 1: Each second, how much further does the older brother run than the younger?
💡Hint 2: He has to run 8 m more than his brother to catch him.
Worked solution
Have a go first, then read the solution step by step.
1.Each second the older runs 4 m and the younger 2 m: the older closes 4 − 2 = 2 m.
2.The younger is 8 m ahead and the gap shrinks by 2 m a second: 8 ÷ 2 = 4, so he is caught after 4 seconds.
⚠️Common mistake: dividing by 4 + 2. Running the same way, the gap closes only by the difference of their speeds.
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