Time and Distance Important Formulas
- Average Speed: When a certain distance is covered at speed u and the same distance is covered at speed v, then the average speed during the whole journey is given byNote: In such questions, distance is not required.
- Traveling same distance with 2 different speeds (Case II): When a person reaches a certain distance with speed u, he gets t1 time late and when he increases his speed by v to cover the same distance, then he still gets late by t2 In this case, the distance is calculated by
- Traveling same distance with 2 different speeds (Case I): When a person covers a certain distance between with speed u, he gets his destination late by time t1 but when he covers the same distance with speed v, he reaches his destination t2 time earlier. The distance between two places is given by
- Chasing a thief: A policeman sees a thief at a distance of d. He starts chasing the thief who is running at a speed of u and policeman is chasing with a speed of v (v > u). In this case, the distance covered by the thief when he is caught by the policeman, is given by
- Two persons A and B start running at the same time in opposite directions from two points and after passing each other they complete their journeys in x and y hours, respectively. Then,
- If a man walks with of his usual speed he takes t hours more to cover a certain distance. Then, the time to cover the same distance with his usual speed (hours)
- A person goes a certain distance with S1 km/h and returns back at speed of S2 km/h. The total time taken for the journey is T The distance traveled (D) is:
- Stoppage time per hour: A person/train travels at an average speed of S1 km/h without any stoppage and with stoppages he covers the same distance at a speed of S2 km/h. Then, (where S1>S2)
- From stations P and Q, two trains start moving towards each other with the speeds of u and v, respectively. When they meet each other, it is found that one train covers distance d more than that of another train. In such cases, distance between stations P and Q is given as
- If two trains leave P for Q at time T1 and T2 and travel with speeds u and v respectively, then the distance d from P, where the two trains meet, is given as
- Overtaking two persons with different speeds: If a train overtakes two persons who are walking with speeds of u and v, respectively in the same direction and passes the two persons completely in T1 and T2 time respectively, then Length of the train where T2>T1
- Trains crossing one another: If two trains A and B start from P and Q towards Q and P, respectively and after passing each other they take T1 and T2 time to reach Q and P, respectively and speed of train A is given as u, then Speed of train B = u
- Crossing a pole: If two trains of equal length and different speeds take t1 and t2 time respectively to cross a pole, then time taken by them to cross each other(T), is Note: We use ‘+’ sign, if trains are moving in opposite directions and ‘-‘ sign, if they are moving in same direction.
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