Speed is a topic which many students fear for PSLE Math. Many of them find the problem sums very challenging and gives up at the sight of the question. However, throughout my years of giving PSLE Math tuition, I discovered that there are a few common scenarios that will appear in the problem sums. Each scenario has its own methods to solve the question. By mastering each scenario, my students are able to handle most of the problem sums related to speed in their PSLE.
Download our Challenging PSLE Speed Problems for FREE. These are questions compiled from past school papers. Click the download button below to download.
Overtaking is one of the most common scenarios for speed. Here are some common strategies when you see this type of question.
– For an object to overtake another object, it must travel at a faster speed… DUH!
– (Very Important) If 2 objects start out from the same point but at different times, the instant when the faster object overtakes the slower object, the distance traveled by both objects are the SAME.
Example: Car A started off first. After 30 minutes, car B started to chase after car A. When car B catches with car A, the distance traveled by both cars are the same.
– (Very Important) The time taken for for the faster object to overtake the slower object is the difference in their distance divide by the difference in their speed.
Example: Car A started off 100 metres ahead of Car B and they started at the same time. Car B is 20 m/s faster than Car A. The time Car B takes to overtake Car A will be 5 seconds (100 ÷ 20).
2. 2 Objects Started at the same time in the same direction
– The faster object will reach the destination first… DUH!
– It is impossible for the slower object to overtake the faster one.
– (Very Important) The distance between the 2 objects will be the difference in their speed multiplied by the time which they traveled.
Example: Car A started at 10 m/s. At the same time, Car B started at 8 m/s in the same direction. After 5 seconds, they will be 10 metres ( (10 – 8 ) × 5 ) apart.
3. 2 Objects Started at the same point in opposite directions (Moving away from each other)
– (Very Important) The distance between them is the sum of their speed multiply by the time taken.
Example: Car A and Car B started from the same point in opposite directions. Car A’s speed is 10 m/s. Car B’s speed is 5 m/s. After 3 seconds, the distance between them will be 45 m ((10 + 5) × 3).
4. 2 Objects Started at the same time in opposite directions (Moving towards each other.)
– (Very Important) The time when they meet is the distance between their starting points divided by the sum of their speeds.
Example: Car A travels towards Car B 900 m away at 20 m/s. At the same time, Car B travels towards Car A at 10 m/s. The time for them to meet each other is 30 seconds. ( 900 ÷ (20 + 10) = 30 )
5. 2 Objects Started at different times in opposite directions ( Moving towards each other.)
– (Very Important) The time when they meet is the total distance minus off the distance which the earlier object has traveled, and divide the answer by the sum of their speeds.
Example: Car A travels towards Car B 700 m away at 20 m/s. After 5 seconds, Car B travels towards Car A at 10 m/s. When Car B started, Car A has already traveled 100 metres. (20 × 5) The time for them to meet is 20 seconds. ( (700 – 100) ÷ (20 + 10) = 20 )
Final Tip: Always draw a timeline to represent the distance between 2 points. It always helps!
How to Draw a Good Timeline:
- Draw a Straight Line to represent the total distance
- If there is a fraction given in the question, break up the line into parts, like a model.
- Draw arrows to show the direction of the objects
- Label the starting time and ending time if given
- Label their speeds if given
- Label the distance if given
Example: At noon, a car travelled from Town A to Town B at a speed of 70 km/h. At the same time, a van travelled from Town B to Town A. At 2 pm, the car and the van were 30 km apart after having passed each other earlier. If the car arrived at Town B at 3 pm, find the time the van would arrive at Town A.
Here is how the timeline looks like:
By Jimmy Ling
Director, Math Tutor at Grade Solution Learning Centre
Before you go, remember to download our Challenging PSLE Speed Problems for FREE. These are questions compiled from past school papers. Click the download button below to download.