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**Some basic formulae:**

· Speed = distance/time

· Time = distance /speed

· If the speed of a body changed in the ratio of ”a:b” ,the time taken changes in the ratio “ b:a” .

· X km/hr = (X)×(5/18) meter/second

· X meter/second = (X)×(18/5) km/hr

**Some theorems:**

**Theorem 1 : **if a certain distance is covered at x km/hr and same distance is covered at y km/hr then average speed during the whole journey is given by = 2xy/(x+y) km/hr.

Applications : this theorem is generally used in equal distance kind of problem. Like a student goes to school at a certain speed and returns to his home a different speed. Then his average speed can be calculated by this method.

and thus the distance between his school to home can also be calculated.

**Theorem 2 : **if travelling at a certain speed a man reaches his workplace ‘x ’ minutes early and if he travels on another speed , he reaches ‘y’ minutes late then distance between his house to office is given by

Require**d **distance = (product of two given speeds / difference of two given speeds ) × difference between arrival times in hours .

**Theorem 3 : : **if travelling at a certain speed a man reaches his workplace and returns at a different a different speed , if the whole journey took ‘x’ hours to complete the journey then

Required distance = (product of two speeds / addition of two speeds) × (total time taken in hours )

Note : the time is always taken according to speed, as if speed is given in km/hr then time will also be taken in hours.

**Theorem 4: **if two persons A and B start at a the same time in opposite directions from two points and after passing each other they complete the journeys in ‘a’ and ‘b’ hrs respectively then

A’s speed : B’s speed = √b : √a

·**Theorem 5: **speed and time are taken inversely proportional therefore S_{1}T_{1} = S_{2}T_{2}= S_{3}T_{3}_{ }…

Where S_{1}, S_{2} , S_{3} are speeds and T_{1}, T_{2}, T_{3} are times taken to travel the same distance.( while the distance is remains fixed or constant.)

**Concepts of relative speeds:**

**Case 1:**

Two bodies are moving in opposite directions at speed *V*1

& *V*2 respectively. The relative speed is defined as *Vr*=*V*1+*V*2

**Case 2:**

Two bodies are moving in same directions at speed *V*1

& *V*2 respectively. The relative speed is defined as *Vr*=|*V*1−*V*2|

- Coming Soon