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Speed · travelling towards each other
P6 · Speed · PSLE Maths
Question
Ali travels by car from Singapore to Kuala Lumpur at 80 km/h. At the same time, Mei Ling travels by car from Kuala Lumpur to Singapore at 70 km/h. The distance between the two cities is 360 km. How long will they take to meet? How far from Singapore will they meet?
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Hint
When two cars travel towards each other, together they cover 80 + 70 km each hour. You can also use the speed ratio 80 : 70 to split 360 km.
Show the answer and step-by-step explanation
Answer: Time taken to meet 2.4 h; Distance from Singapore 192 km
- Draw the distance — First draw the distance from Singapore to Kuala Lumpur as one bar. The whole distance is 360 km.
- Combined speed — The two cars travel towards each other at the same time, so together they cover 80 + 70 km each hour.
- Find the time — Total distance ÷ combined speed = time taken to meet. So 360 ÷ 150 = 2.4 h.
- Split by speed — Before they meet, both travel for the same time. So their distances are in the same ratio as their speeds: 80 : 70 = 8 : 7. The whole distance is 8 + 7 = 15 units.
- Distance from Singapore — 15 units represent 360 km, so 1 unit = 360 ÷ 15 = 24 km. Ali, who started from Singapore, travelled 8 units: 8 × 24 = 192 km.
- Check and recap — Check with the time: 80 × 2.4 = 192 km, 70 × 2.4 = 168 km, and the total is 360 km. 📌 Key idea: for travelling towards each other, use combined speed to find the time first. Then use one speed × time to find the distance from that end.
Method: For travelling towards each other, first find the combined speed: total distance ÷ combined speed = time taken to meet. The distance from one end = speed from that end × time taken.
Practice: 3 similar questions
- Two cars start at the same time from Town A and Town B and travel towards each other. The towns are 240 km apart. The car from Town A travels at 55 km/h, and the car from Town B travels at 65 km/h. How long will they take to meet? How far from Town A will they meet?
Answer
2 h, 110 km — Combined speed = 55 + 65 = 120 km/h. Time taken to meet = 240 ÷ 120 = 2 h. The car from Town A travelled 55 × 2 = 110 km.
- Raju cycles west from East Coast Park at 18 km/h. At the same time, Siti cycles east from another park 45 km away at 12 km/h. How long will they take to meet? How far from East Coast Park will they meet?
Answer
1.5 h, 27 km — Combined speed = 18 + 12 = 30 km/h. Time taken to meet = 45 ÷ 30 = 1.5 h. Raju started from East Coast Park and travelled 18 × 1.5 = 27 km.
- Two coaches start at the same time from Singapore and Kuala Lumpur and travel towards each other. The distance between the two cities is 360 km. The coach from Singapore travels at 80 km/h, and the coach from Kuala Lumpur travels at 64 km/h. How long will they take to meet? How far from Singapore will they meet? After meeting, how much longer will the coach from Singapore take to reach Kuala Lumpur?
Answer
2.5 h, 200 km, 2 h — Combined speed = 80 + 64 = 144 km/h. Time taken to meet = 360 ÷ 144 = 2.5 h. Distance from Singapore = 80 × 2.5 = 200 km. After meeting, the remaining distance is 360 − 200 = 160 km. It will take another 160 ÷ 80 = 2 h to reach Kuala Lumpur.
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