Time, Speed and Distance
Overview
Time, Speed and Distance (TSD) is a foundational arithmetic topic in IBPS PO Prelims that appears in two forms: direct formula-based questions and as part of Data Interpretation sets. Mastery of this topic also unlocks related problems on trains, boats and streams, and races—all of which use the same core relationship.
In the Prelims exam, you can expect 2–4 questions on TSD concepts, often combined with ratio-based shortcuts. The key to scoring here is not just knowing formulas but developing the instinct to convert problems into the basic relationship and apply relative speed concepts quickly. Questions are designed to be solved in under 90 seconds each, so mental math and unit conversion skills are essential.
The entire topic rests on one equation: **Distance = Speed × Time**. Every variation—trains crossing, boats in streams, average speed—is just this equation applied creatively.
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Key Concepts
- **Basic Relationship**: Distance = Speed × Time. Rearrange as needed: Speed = Distance/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 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 "catches up" at this rate.
- **Relative Speed (Opposite Direction)**: When two objects move toward each other, relative speed = sum of their speeds. They approach each other at this combined rate.
- **Trains Crossing**: When a train crosses a stationary object (pole, person), distance covered = length of train. When crossing a platform or another train, distance = sum of both lengths.
- **Boats and Streams**: Downstream speed = boat speed + stream speed. Upstream speed = boat speed − stream speed. Still water speed and stream speed can be derived from these two.
- **Average Speed**: For equal distances at two different speeds, average speed = 2ab/(a+b), not the simple arithmetic mean.
- **Inverse Proportionality**: When distance is constant, speed and time are inversely proportional. If speed doubles, time halves.
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Formulas / Key Facts
| Concept | Formula | |---------|---------| | Basic relation | D = S × T | | km/hr to m/s | Multiply by 5/18 | | m/s to km/hr | Multiply by 18/5 | | Relative speed (same direction) | S₁ − S₂ | | Relative speed (opposite direction) | S₁ + S₂ | | Train crossing pole | Time = Length of train / Speed of train | | Train crossing platform | Time = (Length of train + Length of platform) / Speed | | Two trains crossing each other | Time = (L₁ + L₂) / Relative speed | | Downstream speed | B + S (boat + stream) | | Upstream speed | B − S | | Speed of boat in still water | (Downstream + Upstream) / 2 | | Speed of stream | (Downstream − Upstream) / 2 | | Average speed (equal distances) | 2ab / (a + b) |