TIME AND DISTANCE ...[competitive. exam prep.... topic 2]

TIME AND DISTANCE (Basic concepts)
1. Distance = Speed * Time

2. Time = Distance / Speed

3. Speed = Distance/Time

4. To convert speed in km/h to m/sec, multiply it with 5/18.

5. To convert speed in m/sec to km/h , multiply it with 18/5.

6. If a body travels from point A to point B with a speed of 'p' and back to point A (from point with a speed of ‘q’, then the average speed of the body is:
= 2pq/(p+q).

7. If a car does a journey in 'T' hrs, the first half at 'p' km/hr and the second half at 'q' km/hr. The total distance covered by the car = (2 * Time * p * q ) / (p + q).

8. If a body covers part of the journey at speed p and the remaining part of the journey at a speed q and the distances of the two parts of the journey are in the ratio m : n, then the average speed for the entire journey is:
= (m+n) pq / (mq+np).

9. If a person travelling between two points reaches ‘p’ hours late (If time is given in minutes, it should be converted into hrs by dividing it by 60) travelling at a speed of 'a' km/hr and reaches 'q' km/hr and reaches q hours early travelling at 'b' km/hr, the distance between the two points is:
= (ab/a‐b)(p‐q)

10.If a person goes from 'A' to 'B' at a speed of 'p' kmph and returns at a speed of 'q' kmph and takes 'T' hours in all, then the distance between the A and B:
= Total time taken * (Product of the two Speeds / Addition of the two speeds)

11. If two persons A and B start at the same time in opposite direction from two points and after passing each other they complete the journeys in 'a' and 'b' hrs respectively, then A's speed : B's speed= Square root of b : Square root of a.

12. If A travels certain distance at the rate of 'S1' kmph and B covers the same distance at the rate of 'S2' kmph and if one of them takes 't' minutes longer than the other, then:Distance covered = {(S1 x S2) x Difference in time to cover the distance} / (S1‐S2)

Note :‐ If speed is given kmph and time is given in minutes, then time is to be expressed in hrs. before solving the problem using this formula.

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