MPESB Group · Bite-size lessons
Time and Distance
About 6 min · Mathematics · English
Time worked out from the lesson's 411 words at 150 words a minute, plus a minute for each question.
Time and Distance is a fundamental quantitative topic in MPESB Group 1/2/3 examinations. This topic tests your ability to apply the basic relationship between speed, distance, and time to real-world scenarios involving trains, boats, and moving objects.
Key ideas
- Basic Relationship: Speed = Distance ÷ Time. This single formula, rearranged appropriately, solves most problems. Distance = Speed × Time; Time = Distance ÷ Speed.
- Unit Conversion: To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5. This conversion is essential for train problems where lengths are in metres.
- Relative Speed (Same Direction): When two objects move in the same direction, relative speed = difference of their speeds. The faster object "gains" on the slower one.
- Relative Speed (Opposite Direction): When two objects move towards each other or away from each other, relative speed = sum of their speeds.
- Train Crossing Problems: A train covers its own length when passing a pole/man, but covers (train length + object length) when passing a platform or another train.
Watch out for
- Forgetting to add train length when crossing a platform → When a train crosses any object with length (platform, bridge, another train), always add both lengths to get total distance covered.
- Using wrong relative speed formula → Same direction means subtract speeds; opposite direction means add speeds. Visualize the scenario before calculating.
- Not converting units before calculation → Train lengths are usually in metres, speeds in km/hr. Convert speed to m/s first, then calculate time in seconds.
Quick reference
- Speed = Distance/Time; rearrange as needed for any variable.
- km/hr to m/s: multiply by 5/18 (or divide by 3.6).
- Train crossing pole: Distance = train length only.
- Train crossing platform: Distance = train length + platform length.
- Opposite direction: add speeds. Same direction: subtract speeds.
Check yourself: 3 questions
1. A train travels 120 km at a speed of 40 km/h and the next 180 km at a speed of 60 km/h. What is the average speed of the train for the entire journey?
2. Two trains are running in opposite directions with speeds of 45 km/h and 30 km/h respectively. If the length of each train is 150 meters, in how much time will they cross each other?
3. A boat can travel 36 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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