TNPSC Group II · Bite-size lessons
Time, Speed and Distance
About 6 min · Aptitude and Mental Ability · English
Time worked out from the lesson's 409 words at 150 words a minute, plus a minute for each question.
Time, Speed and Distance (TSD) is a core quantitative aptitude topic. Questions typically involve trains crossing platforms or other trains, boats moving in streams, and problems requiring calculation of average speed over multiple journeys. Mastering TSD is essential because it forms the foundation for related topics like races, circular motion, and clock problems.
Key ideas
- Basic Relationship: Speed = Distance/Time. This can be rearranged to Distance = Speed × Time and Time = Distance/Speed. All TSD problems reduce to manipulating this relationship.
- 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 appears in almost every train problem.
- 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.
- Average Speed: For equal distances at different speeds, average speed = 2ab/(a+b) where a and b are the two speeds. This is the harmonic mean, not the arithmetic mean.
Watch out for
- Using arithmetic mean for average speed → When distances are equal, always use the harmonic mean formula 2ab/(a+b). Arithmetic mean applies only when time spent at each speed is equal.
- Forgetting train length in crossing problems → When a train crosses any object, it must travel its own length completely past the object. Always add train length to stationary object length.
- Wrong relative speed direction → Students often add speeds when trains move in the same direction. Remember: same direction = subtract, opposite direction = add.
Quick reference
- km/hr to m/s: multiply by 5/18
- m/s to km/hr: multiply by 18/5
- Train crosses pole: Time = (Train length)/Speed
- Two trains crossing: Distance = Sum of both lengths
- Boat in still water: (Downstream speed + Upstream speed)/2
Check yourself: 3 questions
1. A train 150 metres long passes a pole in 15 seconds. What is the speed of the train in km/hr?
2. A boat travels 24 km upstream in 4 hours and returns downstream in 3 hours. What is the speed of the stream in km/hr?
3. Two trains of lengths 120 metres and 180 metres are running in opposite directions at speeds of 54 km/hr and 72 km/hr respectively. In how many seconds will they completely cross each other?
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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