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