Topics › Speed › Q104
Speed · moving towards each other
P6 · Speed · PSLE Maths
Question
At East Coast Park, Ali and Mei Ling started at the same time from the two ends of a 1800 m straight cycling track and moved towards each other. Ali cycled at 2.5 m/s and Mei Ling cycled at 3.5 m/s. How many seconds later would they meet? How far was the meeting point from Ali's starting point?
Try it yourself · watch the animation →
Hint
They travel for the same amount of time, so the distances travelled are in the same ratio as their speeds. You can also add the two speeds to find the meeting time.
Show the answer and step-by-step explanation
Answer: Time to meet 300 s; From Ali's starting point 750 m
- Draw the track — First, draw the whole cycling track as one bar: the total length is 1800 m. The meeting point splits it into Ali's distance and Mei Ling's distance.
- Distance ratio — They start at the same time and take the same time to meet. So distance ratio = speed ratio: 2.5 : 3.5 = 5 : 7.
- Find 1 unit — There are 5 + 7 = 12 units altogether, and these 12 units are 1800 m. So 1 unit = 1800 ÷ 12 = 150 m.
- Find meeting point — From Ali's starting point to the meeting point is Ali's 5 units. 5 × 150 = 750 m, so the meeting point is 750 m from Ali's starting point.
- Find the time — Divide Ali's distance by Ali's speed: 750 ÷ 2.5 = 300 s. You can also use combined speed: 1800 ÷ (2.5 + 3.5) = 300 s.
- Check and conclude — Mei Ling's distance is 3.5 × 300 = 1050 m, and 750 m + 1050 m = 1800 m, which is the total distance. 📌 Key idea: for moving towards each other, time to meet = total distance ÷ combined speed; then use speed × time to find the meeting point.
Method: When two people move towards each other, their combined speed is the sum of their speeds. Time to meet = total distance ÷ combined speed. The meeting point can be found using one person's speed × time.
Practice: 3 similar questions
- Siti and Raju started at the same time from the two ends of a 1500 m straight track and ran towards each other. Siti ran at 2 m/s and Raju ran at 3 m/s. How many seconds later would they meet? How far was the meeting point from Siti's starting point?
Answer
300 s, 600 m — Combined speed = 2 + 3 = 5 m/s. Time to meet = 1500 ÷ 5 = 300 s. Siti's distance = 2 × 300 = 600 m, so the meeting point is 600 m from Siti's starting point.
- Mei Ling and Raju started at the same time from the two ends of a 1260 m straight path between the school and the sports hall and walked towards each other. Mei Ling walked at 1.4 m/s and Raju walked at 2.1 m/s. How many seconds later would they meet? How far was the meeting point from Mei Ling's starting point?
Answer
360 s, 504 m — Combined speed = 1.4 + 2.1 = 3.5 m/s. Time to meet = 1260 ÷ 3.5 = 360 s. Mei Ling's distance = 1.4 × 360 = 504 m.
- Ali and Mei Ling were 1500 m apart on a straight path. Ali started first and walked at 2 m/s for 60 s. After that, Mei Ling started from the other end and walked towards him at 3 m/s. How many seconds after Mei Ling started would they meet? How far was the meeting point from Ali's starting point?
Answer
276 s, 672 m — Ali's head start distance = 2 × 60 = 120 m. When Mei Ling started, the distance between them was 1500 − 120 = 1380 m. Combined speed = 2 + 3 = 5 m/s, so the time after Mei Ling started = 1380 ÷ 5 = 276 s. Ali walked for 60 + 276 = 336 s altogether, so his distance = 2 × 336 = 672 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 →