# Time and Distance

We often get questions based on speed, distance and time in UPSC, SSC, CDS and state services exams. Questions in all these exams have almost same level as they intend to judge our analytical ability, we can solve these questions easily if our basic concepts are clear and we have practiced enough variety of questions on those concepts. So lets go through some basic concepts and short tricks for speed, distance and time.

**Speed **: Basically speed is defined as the distance covered by an object in unit time.

**Some basic formulas :**

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__Basic facts to remember __:

- If time is kept constant distance travelled is proportional to the speed of the object
- If speed of object is kept constant, distance travelled is proportional to the time taken
- If the distance covered is kept constant, speed is inversely proportional to the time taken
- If the ratio of two speeds for same distance is a:b then the ratio of time taken to cover the distance is b:a

__Concept of relative speed__ :

- If two objects are moving in same direction with speeds of x and y then their relative speed is (x - y)
- If two objects are moving is opposite direction with speeds of x and y then their relative speed is (x + y)

__Conversion of unit__ :

**km/hr to m/sec conversion:**

**m/sec to km/hr conversion:**

**Shortcut tricks for quicker approach**

** Trick I :** If some distance is travelled at x km/hr and the same distance is travelled at y km/hr then the average speed during the whole journey is given by

** Trick II : **If a person travels a certain distance at X km/hr and returns at Y km/hr, and the total time taken to cover the whole journey is T hours then the one way distance is given by :

** Trick III : **If two persons A and B start their journey at the same time toward each other from two two points P and Q and after crossing each other they take a and b hours in reaching Q and P respectively, then

** Trick IV : **If the same distance is covered at two different speeds S1 and S2 and the time taken to cover the distance are T1 and T2, then the distance is given by :