### 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 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 Now x can be calculated.

Posted Date : 18-09-2021