Time, Speed and Distance
Overview
At the Clerk level, problems are straightforward applications of the basic formula with moderate calculations—you won't encounter the complex multi-variable scenarios seen in PO exams.
This topic branches into three main problem types: basic TSD calculations, train problems (involving length and relative speed), and boats & streams (involving current effects). Mastering TSD requires comfort with unit conversions, relative speed concepts, and quick mental math. Since Clerk Prelims is time-pressured (20 minutes for 35 questions), recognizing problem patterns and applying formulas directly is more valuable than deriving solutions from scratch.
The good news: once you internalize the core formula and its three rearrangements, every TSD problem becomes a matter of identifying what's given and what's asked. Focus on speed and accuracy over complex reasoning.
Key Concepts
- The fundamental relationship: Speed = Distance ÷ Time. This single formula, rearranged three ways, solves every basic TSD problem.
- Unit conversion is non-negotiable: km/hr to m/s requires multiplying by 5/18; m/s to km/hr requires multiplying by 18/5. Mismatched units cause most calculation errors.
- Relative speed determines meeting/crossing problems: When objects move in the same direction, subtract speeds; when moving in opposite directions, add speeds.
- Train problems always involve length: Unlike cars, trains have significant length. The distance covered when crossing an object equals train length plus object length (if the object has length).
- Boats and streams split into upstream and downstream: Downstream speed = boat speed + stream speed; upstream speed = boat speed − stream speed.
- Average speed is not the arithmetic mean: For equal distances at different speeds, use the harmonic mean formula: 2ab/(a+b).
- Inverse proportionality: For constant distance, speed and time are inversely proportional—double the speed means half the time.
Formulas / Key Facts
Basic TSD Formulas
- Speed = Distance / Time
- Distance = Speed × Time
- Time = Distance / Speed
Unit Conversions
- km/hr to m/s: multiply by 5/18
- m/s to km/hr: multiply by 18/5
- 1 km/hr = 5/18 m/s ≈ 0.28 m/s
- 36 km/hr = 10 m/s (memorize this benchmark)
Relative Speed
- Same direction: Relative speed = |S₁ − S₂|
- Opposite direction: Relative speed = S₁ + S₂
Train Problems
- Crossing a pole/person: Distance = Length of train
- Crossing a platform/bridge: Distance = Length of train + Length of platform
- Two trains crossing each other: Distance = Length of train₁ + Length of train₂
Boats and Streams
- Downstream speed = B + S (where B = boat speed in still water, S = stream speed)
- Upstream speed = B − S
- Speed of boat in still water: B = (Downstream + Upstream) / 2
- Speed of stream: S = (Downstream − Upstream) / 2
Average Speed
- For equal distances at speeds a and b: Average speed = 2ab / (a + b)
Worked Examples
Example 1: Basic TSD
Problem: A car travels 240 km in 4 hours. Find its speed in m/s.
Solution:
- Speed = Distance / Time = 240 / 4 = 60 km/hr
- Convert to m/s: 60 × 5/18 = 300/18 = 50/3 = 16.67 m/s
Answer: 16.67 m/s (or 50/3 m/s)
Example 2: Train Crossing a Platform
Problem: A train 150 m long crosses a platform 250 m long in 20 seconds. Find the speed of the train in km/hr.
Solution:
- Total distance covered = Train length + Platform length = 150 + 250 = 400 m
- Time = 20 seconds
- Speed = 400 / 20 = 20 m/s
- Convert to km/hr: 20 × 18/5 = 72 km/hr
Answer: 72 km/hr
Example 3: Boats and Streams
Problem: A boat travels 36 km downstream in 3 hours and returns upstream in 6 hours. Find the speed of the boat in still water and the speed of the stream.
Solution:
- Downstream speed = 36 / 3 = 12 km/hr
- Upstream speed = 36 / 6 = 6 km/hr
- Speed of boat (B) = (12 + 6) / 2 = 9 km/hr
- Speed of stream (S) = (12 − 6) / 2 = 3 km/hr
Answer: Boat speed = 9 km/hr, Stream speed = 3 km/hr
Example 4: Two Trains Crossing
Problem: Two trains of lengths 120 m and 80 m are running in opposite directions at 54 km/hr and 36 km/hr respectively. How long will they take to cross each other?
Solution:
- Total distance = 120 + 80 = 200 m
- Relative speed (opposite directions) = 54 + 36 = 90 km/hr
- Convert to m/s: 90 × 5/18 = 25 m/s
- Time = 200 / 25 = 8 seconds
Answer: 8 seconds
Common Mistakes
- Forgetting unit conversion → Always check if speed is in km/hr and distance in meters (or vice versa). Convert before calculating, not after.
- Adding lengths incorrectly in train problems → When a train crosses a pole or person, only train length matters. Add platform/bridge length only when crossing stationary objects with length.
- Confusing upstream and downstream → Downstream means moving with the current (speeds add); upstream means against the current (subtract stream speed from boat speed).
- Using arithmetic mean for average speed → For a round trip at different speeds, the average speed is 2ab/(a+b), not (a+b)/2. The arithmetic mean only works when times are equal, not distances.
- Wrong relative speed direction → Same direction means subtract (the faster one catches up slowly); opposite direction means add (they approach each other quickly).
- Ignoring that relative speed applies to the combined distance → When two trains cross each other, use relative speed for the combined length, not individual lengths separately.
Quick Reference
- Speed = Distance / Time; rearrange as needed for the unknown.
- km/hr × 5/18 = m/s; m/s × 18/5 = km/hr.
- Same direction: subtract speeds. Opposite direction: add speeds.
- Train crossing platform: Distance = Train length + Platform length.
- Boat in still water = (Downstream + Upstream) / 2.
- Stream speed = (Downstream − Upstream) / 2.