Time and Distance

The relation among distance, time and speed is

                              Distance   =   Speed x Time.
                                     
       If a car covers 50 kilometres in each hour then the speed of the car is 50Kmph.

       If a man travels 10 metres in one second’s time the the speed of the man is 10 mps.
 

Convertion of speeds:         KMPH to MPS

MPS to KMPH
                                 

           ^{When a certain distance is traveled with a speed of x kmph and another equal distance is traveled at y kmph, then the average speed =} 
 

TRAINS
         If a train has to cross a pole or a man or any particular point  then it has to cover a distance equal to its own length.
         If a train has to cross a platform or bridge or tunnel etc. then it has to cover a length equal to its length + platform/bridge/tunnel length.
 

Relative speed
        When two speeds are in opposite direction,
         Relative speed = sum of the speeds.
        When two speeds are in the same direction,
        Relative speed = difference of the speeds.

BOATS AND STREAMS
Still water: water without motion. A boat can travel or a man can swim in that water with their original speeds.
Stream / current : water flow with some speed.
Down stream: along with the flow.
Upstream: against the water flow
If the speed of the boat in still water is b kmph and speed of the current is c kmph respectively, then

                            Downrate ( x )  =   b + c

                            Uprate ( y )       =  b – c
                            

Average speed

      If a moving object travels from A to B at the speed of x km/hr, and from B to A at the speed of y km/hr, then
             
Example 1:  A train 100 metre long is running at the speed of 21 km/hr and another train 150 meter long is running at the speed of 36 km/hr in the same direction. How long will the faster train take to pass the first train?
Solution:  Sum of the length of both the train =  x₁ + x₂ = 100 + 150  = 250 m
                                 Difference of their speeds =  y₁ - y₂   =  21 - 36
                                                                               = 15 km/hr
                                                     

Question with office concern
Example 1:  A person walking at x km/hr reaches his office t₁ minutes late. If he walks at y km/hr, he reaches there t₂ minutes earlier, then
            

Example 5:  A man covers a distance of 160 km at 64 km/hr and next 160 km at 80 km/hr. what is his average speed for his whole journey of 320 km?

Example 6: What will be the length of the train P when it is running at 60 km/hr and crosses another train Q running in opposite direction, in 18 seconds? In order to answer this question which of the statements (a) and (b) is/are sufficient?
              (a) Length of the train Q is 80 meter
              (b)  Speed of the train Q is 90 km/hr
Solution: Both statements (a) and (b) together are necessary
                  '.'  The trains are running in opposite directions

Example 7:  A boat takes 3 hours to go from P to Q downstream and from Q to P up stream. What is the speed of the boat in still water? to know the answer of this  question, the knowledge of which of the statements (a) and (b) is/are sufficient?

The distance between P and Q is 6 km.
The speed of the river is 2 km/hr.
Solution: Both statements (a) and (b) together are necessary to the question.
                  Let the speed of the boat in still water be x km/hr.
            .'.   Speed of the boat down stream = (x + 2) km/hr
       And            Speed of the boat upstream =  (x -2) km/hr