Speed, Time and Distance — One Formula, Six Question Types

One Formula, Three Questions

Every speed question in every paper comes from one relation:

Distance = Speed × Time

Rearranged: Speed = Distance ÷ Time, Time = Distance ÷ Speed.

The formula is never what makes a question hard. Units and the frame of reference do. Two rules fix most of it:

• ›km/h → m/s: multiply by 5/18. m/s → km/h: multiply by 18/5. So 72 km/h = 20 m/s, and 15 m/s = 54 km/h.
• ›When distance is fixed, speed and time are inversely proportional. If speed becomes 3/4 of usual, time becomes 4/3 of usual.

That inverse relation is the most productive idea in the chapter. "Walking at 3/4 of his usual speed he reaches 20 minutes late" is a one-line ratio problem, not a six-line algebra problem.

This chapter is worth 2–4 marks in almost every recruitment paper, and the questions repeat in shape year after year.

1. A train 180 m long crosses an electric pole in 12 seconds. What is its speed in km/h?

2. A man covers the first half of a journey at 30 km/h and the second half at 20 km/h. What is his average speed for the whole journey?

3. Two trains 120 m and 180 m long are running towards each other at 40 km/h and 50 km/h. How long do they take to cross each other completely?

4. A boat covers 20 km downstream in 2 hours and returns the same distance in 4 hours. What is the speed of the boat in still water?

5. Walking at 3/4 of his usual speed, a man reaches his office 20 minutes late. What is his usual time to reach the office?

6. A train running at 72 km/h crosses a platform 250 m long in 20 seconds. What is the length of the train?

7. A speed of 90 km/h is equal to how many metres per second?

8. Two men start walking from the same point in the same direction at 5 km/h and 7 km/h. How far apart are they after 3 hours?