Questions from Time, Speed and Distance in Quantitative Aptitude section appear in all competitive exams including Banking, SSC, MBA, Railway among others. Cracking these questions can be easy if one applies shortcut formula.Find below Important points and Formula that is highly useful in solving questions.

## Time and Distance Important Formulas

**Average Speed:**When a certain distance is covered at speedand the same distance is covered at speed*u*, then the average speed during the whole journey is given by*v***Note:**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, he gets*u***t**time late and when he increases his speed by_{1}to cover the same distance, then he still gets late by*v***t**In this case, the distance is calculated by_{2}**Traveling same distance with 2 different speeds (Case I):**When a person covers a certain distance between with speed, he gets his destination*u***late by time t**but when he covers the same distance with speed_{1}, he reaches his destination*v***t**. The distance between two places is given by_{2}time earlierA policeman sees a thief at a distance of*Chasing a thief:*. He starts chasing the thief who is running at a speed of*d*and policeman is chasing with a speed of*u*(*v**v**>*). In this case, the distance covered by the thief when he is caught by the policeman, is given by**u**- 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
hours more to cover a certain distance. Then, the time to cover the same distance with his usual speed (hours)*t* - A person goes a certain distance with
**S**km/h and returns back at speed of_{1}**S**km/h. The total time taken for the journey is_{2}**T**The distance traveled (D) is: **Stoppage time per hour****:**A person/train travels at an average speed of**S**km/h without any stoppage and with stoppages he covers the same distance at a speed of_{1}**S**km/h. Then, (where S_{2}_{1}>S_{2})

- From stations P and Q, two trains start moving towards each other with the speeds of
and*u*, respectively. When they meet each other, it is found that one train covers distance*v*more than that of another train. In such cases, distance between stations P and Q is given as*d* - If two trains leave P for Q at time
**T**and_{1}**T**and travel with speeds_{2}and*u*respectively, then the distance*v*from P, where the two trains meet, is given as*d* **Overtaking two persons with different speeds:**If a train overtakes two persons who are walking with speeds ofand*u*, respectively in the same direction and passes the two persons completely in*v*and*T*_{1}time respectively, then Length of the train*T*_{2}**where T**_{2}>T_{1}

**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*T*and_{1}*T*time to reach Q and P, respectively and speed of train A is given as_{2}, then*u***Speed of train B =***u*

**Crossing a pole:**If two trains of equal length and different speeds takeand*t*_{1}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.*t*_{2}

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