# Time and Distance Problem

## Time and Distance Problem

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

## Formula

speed = | distance cover |

time taken |

### 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

## Formula

If two objects are moving is opposite direction with speeds of x and y then their relative speed is

## Formula

## Unit Conversion

## km/hr to m/sec conversion

x km/hr = |
x x |
5 | m/sec. | ||

18 |

## m/sec to km/hr conversion

x m/sec = |
x x |
18 | km/hr. | ||

5 |

### Important Shortcut Formulas

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

## average speed

average speed = | 2xy | km/hr | ||

x+y |

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

## one way distance

one way distance = | t |
xy | km | ||

x+y |

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

### Time and Distance Shortcut Methods

**Rule 4: **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