Olympiad topic · P3–P6
Meeting
The basis of journey problems: meeting and catching up appear in the Hua Xia Cup's P4 to P6 qualifying rounds and finals.
Try one
★★ MediumMing's home and his school are on the same straight road, 460 m apart.
When school ends, Ming walks home; at the same moment his mother leaves home along the same road to meet him.
Ming walks 55 m a minute and his mother 60 m a minute.
When they meet, how far has his mother walked?
- Hint 1: To know how far his mother walked, first find for how many minutes she walked.
- Hint 2: How much closer do they get each minute?
- 1.Each minute his mother walks 60 m and Ming 55 m: together they close 60 + 55 = 115 m.
- 2.The 460 m gap shrinks by 115 m a minute: 460 ÷ 115 = 4, so they meet after 4 minutes.
- 3.His mother walked for 4 minutes: 60 × 4 = 240 m.
- ⚠️Common mistake: assuming they meet halfway. Their speeds differ, so the faster walker covers more.
Answer: 240 m
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsOne meeting or one catch-up.
- ★★MediumFree3 question types · unlimited questionsOne sets off first.
- ★★★HardFree3 question types · unlimited questionsA dog running to and fro, or one covering more by the meeting.
- ★★★★Expert (competition level)VIP3 question types · unlimited questionsThe second meeting, a circular track.
Meeting: what it is and how to solve it
Two people heading towards each other (meeting), or the same way at different speeds (catching up): find the time or distance.
For example: Two children 63 m apart run towards each other at 6 m and 3 m a second. When do they meet? 63 ÷ (6 + 3) = 7 seconds.
The key idea: Meeting: the distance they cover together = sum of speeds × time; catching up: the gap closed = difference of speeds × time. Draw a line with both starting points and directions. It's the usual method's distance = speed × time, with the two speeds taken together.
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