Time, Speed and Distance — Study Notes

Overview

Time, Speed and Distance (TSD) problems are a staple of SSC CHSL Tier 1 Quantitative Aptitude. Expect 3–5 questions directly testing these concepts. The topic extends beyond basic motion to trains crossing platforms, boats navigating rivers, and objects moving in the same or opposite directions. Mastery requires understanding the fundamental relationship Distance = Speed × Time and applying it under different scenarios: relative motion, average speed calculations, and water-current adjustments.

CHSL favors straightforward numerical problems over complex multi-step reasoning. You'll encounter trains of given lengths crossing poles or platforms, boats traveling upstream/downstream, and two people/vehicles meeting or overtaking. The key skill is correctly setting up the equation by identifying what distance is actually being covered and what effective speed applies. Most questions test formula application and unit conversion (km/h ↔ m/s) more than conceptual depth.

Common question types include calculating meeting time, overtaking distance, train crossing duration, and boat speed in still water. A strong grip on relative speed and the boats-and-streams formula will unlock most marks in this topic.

Key Concepts

• **Fundamental Relation**: Distance = Speed × Time. Any one variable can be derived if the other two are known. This triplet forms the backbone of every TSD problem.

• **Unit Conversion**: Always align units. To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5. Most errors stem from mixing km and meters or hours and seconds.

• **Relative Speed (Same Direction)**: When two objects move in the same direction, their relative speed = |Speed₁ − Speed₂|. Use this to find overtaking time or the time gap between them.

• **Relative Speed (Opposite Direction)**: When two objects move toward each other, their relative speed = Speed₁ + Speed₂. This is used in meeting-time problems.

• **Average Speed**: Average speed ≠ average of speeds. Average speed = Total Distance / Total Time. For equal distances at two different speeds s₁ and s₂, average speed = (2 × s₁ × s₂) / (s₁ + s₂).

• **Trains**: A train crosses a stationary object (pole, man) in time = Length of train / Speed of train. A train crosses a platform/bridge in time = (Length of train + Length of platform) / Speed of train.

• **Boats and Streams**: Let boat speed in still water = b, stream speed = s. Downstream speed = b + s, Upstream speed = b − s. From these: b = (Downstream + Upstream)/2 and s = (Downstream − Upstream)/2.

• **Speed in still water and stream speed** can always be extracted if you know downstream and upstream speeds or distances and times for both.

Formulas / Key Facts

1. **Distance = Speed × Time** — The universal base formula. 2. **Speed = Distance / Time** — Rearrangement to find speed. 3. **Time = Distance / Speed** — Rearrangement to find time. 4. **km/h to m/s**: Multiply by 5/18. 5. **m/s to km/h**: Multiply by 18/5. 6. **Relative Speed (Opposite Directions)**: S₁ + S₂. 7. **Relative Speed (Same Direction)**: |S₁ − S₂|. 8. **Average Speed (Equal Distances)**: (2 × s₁ × s₂) / (s₁ + s₂). 9. **Average Speed (General)**: Total Distance / Total Time. 10. **Train Crossing Pole**: Time = Length of Train / Speed. 11. **Train Crossing Platform**: Time = (Length of Train + Length of Platform) / Speed. 12. **Downstream Speed**: b + s (boat speed + stream speed). 13. **Upstream Speed**: b − s (boat speed − stream speed). 14. **Boat Speed in Still Water**: (Downstream + Upstream) / 2. 15. **Stream Speed**: (Downstream − Upstream) / 2.

Worked Examples

**Example 1: Basic Speed Calculation** A car covers 300 km in 5 hours. What is its speed in m/s?

**Solution**: Speed = Distance / Time = 300 / 5 = 60 km/h. Convert to m/s: 60 × 5/18 = 300/18 = 50/3 ≈ 16.67 m/s.

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**Example 2: Train Crossing a Platform** A 150 m long train crosses a 250 m platform in 20 seconds. Find the speed of the train in km/h.

**Solution**: Total distance covered = Length of train + Length of platform = 150 + 250 = 400 m. Time = 20 seconds. Speed = 400 / 20 = 20 m/s. Convert to km/h: 20 × 18/5 = 72 km/h.

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**Example 3: Boats and Streams** A boat travels 60 km downstream in 3 hours and returns upstream in 5 hours. Find the speed of the boat in still water and the speed of the stream.

**Solution**: Downstream speed = 60 / 3 = 20 km/h. Upstream speed = 60 / 5 = 12 km/h. Boat speed in still water (b) = (20 + 12) / 2 = 16 km/h. Stream speed (s) = (20 − 12) / 2 = 4 km/h.

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**Example 4: Relative Speed (Meeting)** Two trains 200 km apart travel toward each other at 50 km/h and 70 km/h. When will they meet?

**Solution**: Relative speed = 50 + 70 = 120 km/h. Time to meet = Distance / Relative speed = 200 / 120 = 5/3 hours = 1 hour 40 minutes.

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**Example 5: Average Speed** A person travels 120 km at 60 km/h and returns at 40 km/h. What is the average speed for the whole journey?

**Solution**: Use the equal-distance formula: Average speed = (2 × 60 × 40) / (60 + 40) = 4800 / 100 = 48 km/h.

Common Mistakes

• **Averaging speeds directly**: Students often add two speeds and divide by 2 to find average speed. Correct approach: use total distance / total time or the harmonic mean formula for equal distances.

• **Forgetting to add train and platform lengths**: When a train crosses a platform, the distance is the sum of both lengths, not just the platform. Always read "crosses" carefully.

• **Unit mismatch**: Mixing km and m or hours and seconds without conversion leads to wrong answers. Always convert to a common unit system before calculating.

• **Confusing downstream and upstream**: Remember downstream is with the current (b + s, faster), upstream is against it (b − s, slower). Reversing these flips the entire solution.

• **Using wrong relative speed direction**: If two objects move in the same direction, subtract speeds. If they move toward each other, add speeds. Mixing these gives incorrect meeting or overtaking times.

Quick Reference

• **Basic formula**: Distance = Speed × Time.
• **km/h to m/s**: Multiply by 5/18; reverse: multiply by 18/5.
• **Train crossing pole**: Time = Train Length / Speed.
• **Train crossing platform**: Time = (Train + Platform) / Speed.
• **Downstream**: b + s; Upstream: b − s.
• **Boat in still water**: (Down + Up)/2; Stream: (Down − Up)/2.
• **Relative speed**: Same direction → subtract; Opposite → add.
• **Average speed (equal distance)**: 2s₁s₂/(s₁ + s₂).