Time and Distance — SSC GD Study Notes

Overview

Time and Distance is a high-scoring topic in SSC GD Elementary Mathematics. Every year, expect 2–3 direct questions on speed, average speed, trains, and boats-and-streams. The topic tests your ability to convert units, apply the fundamental formula, and handle relative motion scenarios. Mastering this section gives you quick marks because once you learn the standard patterns, most problems solve in under 60 seconds.

The key to success is understanding the single core relationship: **Distance = Speed × Time**. All variations — average speed, train crossing, boats moving upstream or downstream — simply rearrange or extend this formula. Focus on unit conversions (km/h ↔ m/s) and recognise problem types quickly. With 15–20 practice problems across each sub-topic, you'll develop the speed and accuracy needed for exam conditions.

Common mistakes include forgetting unit conversions, confusing relative speeds, and misapplying average speed formulas. The notes below address these traps directly.

Key Concepts

• **Fundamental Relationship**: Distance = Speed × Time. Every problem boils down to finding one quantity when the other two are known.
• **Unit Conversion**: 1 km/h = 5/18 m/s. Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h. Trains and platform problems almost always need m/s.
• **Average Speed**: When distances are equal, average speed = 2xy/(x+y) where x and y are the two speeds. When times are equal, average speed is the simple arithmetic mean (x+y)/2. Never just average speeds blindly.
• **Relative Speed**: When two objects move in the same direction, relative speed = |Speed₁ − Speed₂|. When moving toward each other (opposite directions), relative speed = Speed₁ + Speed₂.
• **Train Problems**: Length of train matters. Time to cross a pole/man = (Length of train) / (Speed of train). Time to cross a platform = (Length of train + Length of platform) / (Speed of train).
• **Boats and Streams**: Speed in still water = b, stream speed = s. Downstream speed = b + s, upstream speed = b − s. If downstream and upstream speeds are given, still water speed = (downstream + upstream)/2 and stream speed = (downstream − upstream)/2.
• **Meeting and Crossing**: If two objects start simultaneously from opposite ends, time to meet = (Total distance) / (Sum of speeds). If they start from the same point moving in the same direction, time for faster to lap = (Initial gap) / (Difference in speeds).
• **Return Journey**: If a person travels to a place at speed x and returns at speed y, the average speed for the whole journey is 2xy/(x+y), not (x+y)/2.

Formulas / Key Facts

1. **Distance = Speed × Time** — Core formula. Rearrange as Speed = Distance/Time or Time = Distance/Speed. 2. **Conversion: km/h to m/s** — Multiply by 5/18. Example: 72 km/h = 72 × 5/18 = 20 m/s. 3. **Conversion: m/s to km/h** — Multiply by 18/5. Example: 15 m/s = 15 × 18/5 = 54 km/h. 4. **Average Speed (equal distances)** — Average speed = 2xy/(x+y) if distances covered at speeds x and y are equal. 5. **Average Speed (equal times)** — Average speed = (x+y)/2 if time spent at speeds x and y are equal. 6. **Relative Speed (same direction)** — Relative speed = Speed₁ − Speed₂. 7. **Relative Speed (opposite direction)** — Relative speed = Speed₁ + Speed₂. 8. **Train crossing a pole** — Time = Length of train / Speed of train. 9. **Train crossing a platform** — Time = (Length of train + Length of platform) / Speed of train. 10. **Two trains crossing each other** — Time = (Length₁ + Length₂) / Relative speed. 11. **Downstream speed** — b + s (b = boat speed in still water, s = stream speed). 12. **Upstream speed** — b − s. 13. **Still water and stream speed from downstream/upstream** — b = (downstream + upstream)/2 and s = (downstream − upstream)/2.