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Changing speed midway · find each time
P6 · Speed · PSLE Maths
Question
Raju cycled from home to the Sports Hub, a distance of 3900 m. He cycled the first part at 4 m/s and then increased his speed to 6 m/s for the remaining distance. He took 750 s altogether. How long did Raju cycle at 4 m/s and at 6 m/s respectively?
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Hint
First suppose he cycled the whole trip at 4 m/s. Find how many metres short he would be; this shortfall comes from the extra speed each second.
Show the answer and step-by-step explanation
Answer: At 4 m/s 300 s; At 6 m/s 450 s
- Draw the distance — First draw a distance model for the whole 3900 m. The first part is at 4 m/s, and the remaining part is at 6 m/s.
- Suppose all slow — If Raju cycled the whole 750 s at 4 m/s, he would cover: 4 × 750 = 3000 m.
- Find extra distance — The actual distance is 3900 m, which is 900 m more than 3000 m. This extra 900 m is gained because he cycled faster in the later part.
- Use speed difference — In the faster part, each 1 s gives an extra: 6 − 4 = 2 m. To gain 900 m, the time needed is 900 ÷ 2 = 450 s.
- Find slow time — So he cycled at 6 m/s for 450 s. The total time was 750 s, so the slower time is 750 − 450 = 300 s. Check: 4 × 300 = 1200 m, and 6 × 450 = 2700 m; together they make 3900 m. 📌 Key idea: for a speed change question, suppose the whole trip is at the slower speed first. Then use extra distance ÷ difference in speed to find the faster time.
Method: Draw a distance model split into the slower part and the faster part. Use the “suppose all at the slower speed” method to find the extra distance, then divide by the difference in speed to get the faster time.
Practice: 3 similar questions
- Mei Ling travelled 1200 m from school to the MRT station. She walked the first part at 1.5 m/s and jogged the remaining distance at 2.5 m/s. She took 600 s altogether. How long did she walk and jog respectively?
Answer
300 s, 300 s — Suppose the whole journey was at 1.5 m/s: 1.5 × 600 = 900 m. Extra distance covered: 1200 − 900 = 300 m. Jogging gives an extra 2.5 − 1.5 = 1 m each second. Jogging time = 300 ÷ 1 = 300 s. Walking time = 600 − 300 = 300 s.
- Ali cycled 5600 m along the park connector. He cycled the first part at 5 m/s and the remaining distance at 7 m/s. The whole trip took 900 s. How long did Ali cycle at each speed?
Answer
350 s, 550 s — Suppose the whole trip was at 5 m/s: 5 × 900 = 4500 m. Extra distance covered: 5600 − 4500 = 1100 m. Difference in speed: 7 − 5 = 2 m/s. Faster time = 1100 ÷ 2 = 550 s. Slower time = 900 − 550 = 350 s.
- Siti skated 2880 m to the community centre. She skated the first part at 3 m/s and increased her speed by 50% for the remaining distance. The whole trip took 720 s. How long did she skate at each speed?
Answer
240 s, 480 s — Increased speed = 3 + 50% × 3 = 4.5 m/s. Suppose the whole trip was at 3 m/s: 3 × 720 = 2160 m. Extra distance covered: 2880 − 2160 = 720 m. Difference in speed: 4.5 − 3 = 1.5 m/s. Time after speeding up = 720 ÷ 1.5 = 480 s. Time at the original speed = 720 − 480 = 240 s.
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