Time, work, speed, distance and trains

Key Points at a Glance

1. 1

   Speed formula: speed = distance / time; therefore distance = speed x time and time = distance / speed.

2. 2

   Unit conversion rule: 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h; convert before combining quantities.

3. 3

   Average speed rule: average speed is total distance divided by total time; for equal distances at speeds a and b, use 2ab / (a + b).

4. 4

   Relative speed rule: objects moving in opposite directions have relative speed equal to the sum of speeds; objects moving in the same direction have relative speed equal to the difference of speeds.

5. 5

   Work formula: if a person completes a job in n days, one day's work = 1/n of the job; combined work is the sum of individual one-day rates.

6. 6

   Efficiency rule: for the same job, time and efficiency are inversely proportional; a worker with double efficiency takes half the time.

7. 7

   Train crossing rule: time taken = distance to be covered / relative speed; for crossing a pole use train length, and for crossing a platform use train length + platform length.

8. 8

   Pipe-and-cistern method: filling rates are positive, emptying rates are negative, and the net rate decides the total filling or emptying time.