UP Police Constable · Bite-size lessons
Time and Distance
About 6 min · Numerical & Mental Ability · English
Time worked out from the lesson's 357 words at 150 words a minute, plus a minute for each question.
Time and Distance is a topic in the Numerical & Mental Ability section of UP Police Constable exam. The topic tests your ability to apply the fundamental relationship between speed, distance and time in various real-world scenarios.
Key ideas
- Basic relationship: Distance = Speed × Time. Any two known quantities give you the third. Speed is measured in km/hr or m/s; always convert units when mixing them.
- Speed 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 appears in almost every train problem.
- Average speed: When a person travels different distances at different speeds, average speed = Total Distance ÷ Total Time. Never calculate average speed as the arithmetic mean of two speeds unless times are equal.
- Relative speed: When two objects move in the same direction, relative speed = difference of speeds. When moving in opposite directions, relative speed = sum of speeds. This applies to trains passing each other and boats in streams.
- Trains: A train must cover its own length plus any platform/bridge/pole length. Time to cross = (Train length + Object length) ÷ Speed. When two trains cross each other, consider sum of their lengths.
Quick reference
- D = S × T: Master this and rearrange instantly for any unknown.
- km/hr to m/s: multiply by 5/18; m/s to km/hr: multiply by 18/5.
- Average speed ≠ average of speeds unless times are equal.
- Relative speed: Same direction → subtract; opposite direction → add.
- Train crossing: Distance = train length + object length.
Check yourself: 3 questions
1. A train 120 metres long is running at a speed of 54 km/hr. How much time will it take to cross a pole?
2. A boat travels 30 km upstream in 5 hours and the same distance downstream in 3 hours. What is the speed of the boat in still water?
3. Two trains of lengths 150 metres and 200 metres are running in opposite directions at speeds of 45 km/hr and 54 km/hr respectively. In how much time will they cross each other?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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