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Aptitude · Lesson 6 of 9

Time, speed & distance

Speed formula, unit conversion, average speed, relative speed and trains.

  • Distance = Speed × Time.
  • km/h → m/s: multiply by 5/18; m/s → km/h: multiply by 18/5.
  • Average speed for equal distances at speeds a and b = 2ab / (a + b) — not (a+b)/2.
  • Relative speed: opposite directions add, same direction subtract.
  • A train crossing a pole covers its own length; crossing a platform covers train + platform length.
  • Boats: downstream = boat + stream; upstream = boat − stream.

Example: A bus goes from Kochi to Thrissur at 60 km/h and returns at 40 km/h. Find the average speed.

  1. Equal distances → 2ab/(a+b).
  2. 2 × 60 × 40 / 100 = 4800/100.

Answer: 48 km/h

Example: A 200 m train runs at 72 km/h. How long does it take to cross a 300 m platform?

  1. Speed = 72 × 5/18 = 20 m/s.
  2. Distance = 200 + 300 = 500 m.
  3. Time = 500 / 20.

Answer: 25 seconds

Key points

  • Convert units first (×5/18).
  • Equal distances: average speed = 2ab/(a+b).
  • Opposite directions add speeds; same direction subtract.

Quick check

54 km/h equals…

Practice task

Two trains 150 m and 100 m long run in opposite directions at 54 km/h and 36 km/h. How long to cross each other?

Show answer

Relative speed = 90 km/h = 25 m/s; distance = 250 m; time = 10 seconds.

Interview corner

Why isn't average speed simply the mean of two speeds?

You spend more time at the slower speed, so it carries more weight. Use total distance / total time.

A man walks at 5 km/h and reaches 10 minutes late; at 6 km/h he is 5 minutes early. Distance?

Time difference 15 min = ¼ h. d/5 − d/6 = ¼ → d/30 = ¼ → d = 7.5 km.

Original lesson written by the InfoparkDaily team · © 2026 InfoparkDaily · Free to learn — no paid course or subscription.