# Time and Distance Shortcut Methods

The terms time and distance are related to the speed of a moving object.

**Some Important Facts**

**Distance travelled is proportional to the speed of the object if the time is kept constant.**

Distance travelled is proportional to the time taken if speed of object is kept constant.

Speed is inversely proportional to the time taken if the distance covered is kept constant.

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

**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)**

**Rule 1:**

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

Example

**Rule 2:**

If a person travels a certain distance at x km/hr and returns at y km/hr, if the time taken to the whole journey is T hours then the one way distance is given by

Example

**Rule 3:**

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

Example

**Two persons Ram and Lakhan start their journey from two different places towards each other’s place. After crossing each other, they complete their journey in 1 and 4 hours respectively. Find speed of Lakhan if speed of ram is 20 km/hr.**

**Sol:**

**Rule 4:**

If the same distance is covered at two different speeds S

_{1}and S

_{2}and the time taken to cover the distance are T

_{1}and T

_{2}, then the distance is given by