Time, Speed and Distance — Study Notes

Overview

Time, Speed and Distance (TSD) forms a cornerstone of the Numerical Ability section in SSC MTS Paper 1, typically accounting for 3–5 questions per exam. This topic tests your ability to connect three fundamental quantities: the distance traveled, the speed of movement, and the time taken. While the basic relationship is straightforward, SSC MTS questions add layers of complexity through scenarios involving trains crossing platforms, boats moving in rivers with currents, and problems involving relative motion between two objects.

Mastery of this topic requires comfort with unit conversions (km/h to m/s), fractional and percentage-based speed changes, and the discipline to draw quick diagrams for train and boat problems. The good news: once you internalize the core formulas and practice 20–30 problems, pattern recognition kicks in and most questions become routine applications. The topic also overlaps with ratio-proportion thinking, so a solid grasp here strengthens your overall quantitative reasoning.

Expect direct calculation questions (find speed given distance and time), train problems (crossing poles, platforms, or other trains), boat-stream problems (upstream/downstream speeds), and relative speed scenarios (two objects moving toward or away from each other). Every question is solvable in under 90 seconds if you know the right formula and avoid unit-conversion mistakes.

Key Concepts

• **The fundamental relationship**: Distance = Speed × Time. Any problem in this topic is a manipulation of these three variables. If two are given, the third can always be found.

• **Unit consistency is non-negotiable**: Speed in km/h with time in hours gives distance in km. Speed in m/s with time in seconds gives distance in meters. The most common error is mixing units without conversion.

• **Conversion between km/h and m/s**: To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5. Memorize this — it appears in nearly every train problem.

• **Relative speed depends on direction**: When two objects move in the same direction, relative speed = difference of speeds. When moving toward each other (opposite directions), relative speed = sum of speeds.

• **Boats and streams introduce effective speeds**: A boat's speed in still water is its own speed. Downstream speed = boat speed + stream speed. Upstream speed = boat speed − stream speed. The stream helps downstream, opposes upstream.

• **Train problems require visualizing lengths**: A train crossing a stationary point (pole, man) covers its own length. A train crossing a platform covers train length + platform length. Two trains crossing each other cover the sum of both lengths.