Time, Speed and Distance

Overview

Time, Speed and Distance (TSD) is a cornerstone topic in the TN TET Mathematics section, appearing consistently in both Paper I and Paper II. This topic tests your ability to apply a single fundamental relationship across varied real-world contexts—moving trains, boats in streams, and journeys with varying speeds.

Mastery here requires comfort with unit conversions, the ability to set up equations from word problems, and recognising which formula variant applies to a given scenario. The good news: once you internalise the core formula and its rearrangements, every problem becomes a structured exercise rather than a puzzle. Expect 2–4 questions from this area, often combining TSD with ratio or algebra concepts.

Key Concepts

• **The fundamental relationship**: Distance = Speed × Time. All TSD problems derive from rearranging this single equation.

• **Unit consistency is critical**: Speed in km/hr with time in hours gives distance in km. Mixing units (minutes with km/hr) is the most common source of errors.

• **Conversion factors**: To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

• **Relative speed for same-direction motion**: When two objects move in the same direction, relative speed = difference of their speeds.

• **Relative speed for opposite-direction motion**: When objects move towards each other, relative speed = sum of their speeds.

• **Boats and streams**: Downstream speed = boat speed + stream speed. Upstream speed = boat speed − stream speed.

• **Average speed for equal distances**: When the same distance is covered at two different speeds, average speed = 2ab/(a+b), not the arithmetic mean.

• **Train problems are length problems**: A train crossing a platform or another train must cover the combined lengths of both objects.

Formulas / Key Facts

| Formula | Context | |---------|---------| | Distance = Speed × Time | Core relationship | | Speed = Distance / Time | Finding rate of travel | | Time = Distance / Speed | Finding duration | | km/hr to m/s: multiply by 5/18 | Unit conversion | | m/s to km/hr: multiply by 18/5 | Unit conversion | | Downstream speed = B + S | Boat speed B, stream speed S | | Upstream speed = B − S | Boat speed B, stream speed S | | Boat speed in still water = (Downstream + Upstream)/2 | Deriving boat's own speed | | Stream speed = (Downstream − Upstream)/2 | Deriving current speed | | Average speed (equal distances) = 2ab/(a+b) | Speeds a and b for same distance | | Time to cross = (Length of train + Length of object) / Speed | Train crossing platform/bridge/another train | | Time to cross a person/pole = Length of train / Speed | Object of negligible length |