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 = 2xy/x+y
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.
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
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
Now x can be calculated.