Key facts

  • In time-speed-distance questions, the base relation is distance = speed × time; use it only after bringing all units to the same system.
  • To convert km/h into m/s, multiply by 5/18; to convert m/s into km/h, multiply by 18/5.
  • Relative speed is added when two bodies move in opposite directions and subtracted when they move in the same direction.
  • Average speed is total distance divided by total time; it is not usually the simple average of the given speeds.
  • For trains, use the total distance to be cleared: train length alone for a pole, and train length plus platform length for a platform.

Key Points at a Glance

  1. 1

    In time-speed-distance questions, the base relation is distance = speed × time; use it only after bringing all units to the same system.

  2. 2

    To convert km/h into m/s, multiply by 5/18; to convert m/s into km/h, multiply by 18/5.

  3. 3

    Relative speed is added when two bodies move in opposite directions and subtracted when they move in the same direction.

  4. 4

    Average speed is total distance divided by total time; it is not usually the simple average of the given speeds.

  5. 5

    For trains, use the total distance to be cleared: train length alone for a pole, and train length plus platform length for a platform.

  6. 6

    In time and work, treat one complete job as 1; if A finishes in x days, A's one-day work is 1/x.

  7. 7

    Combined work is found by adding rates, not by adding days; this is the most common reciprocal trap.

  8. 8

    Pipes, cisterns and leakage questions are also work-rate questions: filling rates are positive and emptying rates are negative.

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Core relation and unit discipline

Time-speed-distance questions are built on one simple relation: distance = speed × time. The other two forms come from the same relation: speed = distance/time and time = distance/speed. CET questions usually test whether you select the correct form quickly and keep the units consistent.

If speed is in km/h and time is in hours, distance comes in kilometres. If speed is in m/s and time is in seconds, distance comes in metres. Do not multiply 60 km/h directly by 20 seconds. First convert either 60 km/h into m/s or 20 seconds into hours. This small unit discipline prevents many wrong options.

The standard conversions are:

  • km/h to m/s: multiply by 5/18.
  • m/s to km/h: multiply by 18/5.

Example: a bus travels at 54 km/h for 40 seconds. Convert 54 km/h into m/s: 54 × 5/18 = 15 m/s. Distance = 15 × 40 = 600 m.

Another example: a runner covers 200 m in 25 seconds. Speed = 200/25 = 8 m/s. In km/h, speed = 8 × 18/5 = 28.8 km/h.

For MCQs, first underline what is asked: distance, speed or time. Then check the units. If the answer choices are in metres but your working gives kilometres, the numerical value may look tempting but still be wrong.

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