Time, Speed and Distance — Study Notes

Overview

Time, Speed and Distance is a high-yield topic in SSC CGL Tier-1, appearing in 2–4 questions per exam. The topic tests your ability to manipulate the fundamental relationship **Distance = Speed × Time** and apply it to real-world scenarios involving trains crossing objects, boats moving in rivers, and relative motion between two moving bodies.

Mastery requires fluency in unit conversions (especially km/h ↔ m/s), recognizing problem patterns, and executing calculations quickly. Most questions involve either trains (crossing platforms, poles, or other trains), boats and streams (upstream/downstream speed adjustments), or relative speed (two objects moving toward or away from each other). Average speed problems test weighted averaging when speeds change across segments.

Strong command of this topic directly translates to marks because the problems follow predictable templates. Focus on speed of calculation and recognizing which formula applies instantly.

Key Concepts

• **Fundamental relationship**: Distance = Speed × Time. Any one quantity can be found if the other two are known. Rearrange as Speed = Distance/Time or Time = Distance/Speed as needed.

• **Unit conversion**: 1 km/h = 5/18 m/s. To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5. This is critical for train problems where lengths are in meters and speeds in km/h.

• **Relative speed — same direction**: When two objects move in the same direction, their relative speed is the difference of their speeds (Speed₁ − Speed₂). Used when one train overtakes another.

• **Relative speed — opposite direction**: When two objects move toward each other, their relative speed is the sum of their speeds (Speed₁ + Speed₂). Used when two trains cross each other head-on.

• **Train crossing problems**: When a train crosses a stationary object (pole, man), the distance covered equals the length of the train. When crossing a platform or bridge, distance = length of train + length of platform/bridge.

• **Boats and streams**: Let speed of boat in still water = b km/h and speed of stream = s km/h. Then upstream speed = (b − s) km/h and downstream speed = (b + s) km/h. The stream opposes upstream motion and aids downstream motion.

• **Average speed**: Average speed is **not** the arithmetic mean of speeds. It equals Total Distance / Total Time. For equal distances at two speeds, use the harmonic mean formula: Average Speed = (2 × Speed₁ × Speed₂) / (Speed₁ + Speed₂).

• **Meeting and crossing time**: If two objects start from opposite ends and meet, time to meet = Total Distance / (Speed₁ + Speed₂). If they start from the same point moving in opposite directions, they separate at relative speed (Speed₁ + Speed₂).