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.