Topics › Speed › Q130
Speed · catch-up
P6 · Speed · PSLE Maths
Question
Mei Ling started walking from the void deck to the MRT station along the same route at 75 m/min. 12 min later, Ali started cycling from the same place at 225 m/min. How many minutes after Ali started did he catch up with Mei Ling?
Try it yourself · watch the animation →
Hint
First find Mei Ling's head start distance, then use the difference in their speeds to close this distance gap.
Show the answer and step-by-step explanation
Answer: After Ali started 6 min
- Draw head start — Mei Ling walked for 12 min first. Let each small unit show the distance she walks in 1 min.
- Find the head start — Mei Ling's speed is 75 m/min. So in 12 min, her head start distance is 900 m.
- Compare speeds — Ali cycles 225 m each minute, while Mei Ling walks 75 m each minute. The distance Ali gains each minute is the difference in their speeds.
- Find catch-up time — The head start distance is 900 m. Ali gains 150 m each minute. So we divide 900 by 150.
- Check and recap — Ali's distance in 6 min: 225 × 6 = 1350 m. Mei Ling walks for 18 min in total: 75 × 18 = 1350 m. The distances are the same, so Ali catches up. 📌 Key idea: For same-direction catch-up, use head start distance ÷ difference in speeds.
Method: For catch-up in the same direction: head start distance = slower person's speed × head start time; catch-up time = head start distance ÷ difference in speeds.
Practice: 3 similar questions
- Raju walked from the void deck to the playground at 90 m/min. 8 min later, Siti cycled from the same place along the same route at 210 m/min. How many minutes after Siti started did she catch up with Raju?
Answer
6 min — Raju's head start distance is 90 × 8 = 720 m. The difference in speeds is 210 − 90 = 120 m/min. Catch-up time = 720 ÷ 120 = 6 min.
- On a park connector, Siti jogged at 100 m/min. 18 min later, Raju cycled from the same point in the same direction at 250 m/min. How long after Raju started did he catch up with Siti?
Answer
12 min — Siti's head start distance is 100 × 18 = 1800 m. Raju gains 250 − 100 = 150 m each minute. Catch-up time = 1800 ÷ 150 = 12 min.
- Ali walked from the school gate to East Coast Park at 70 m/min. 18 min later, Mei Ling cycled from the same school gate along the same route at 250 m/min. How far from the school gate were they when Mei Ling caught up with Ali?
Answer
1750 m — Ali's head start distance is 70 × 18 = 1260 m. Mei Ling gains 250 − 70 = 180 m each minute. Catch-up time = 1260 ÷ 180 = 7 min. Distance from the school gate = 250 × 7 = 1750 m.
Learn it on classai
An animation walks through each step, then 3 similar questions check it stuck; mistakes come back for review after 1, 3 and 7 days.
Open this question →