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Concept - Speed & Time


 

Some Important Formulas:


Speed & Time !

 

 

 

If the speed of two trains are in the ratio of x:y, then the ratio of time taken cover a certain distance by them = 1/x : 1/y  i.e. y:x

1km per hour = 5/8 meter per second


1 meter per second = 18/5 km per hour

Whenever train crosses a tree, a telegraph post , or a standing man :- distance = length of the train
Whenever train crosses a bridge, or a plot form or a another train,

Distance = length of train + length of bridge
=length of train + length of plot form
=length of 1st train + length of 2nd train

 

Moving Trains:-
If two trains are moving in the same direction, their relative speed is equal to difference of their speed.
If two trains are moving in the opposite direction, their relative speed is equal to sum of their speeds.
If a person goes from A to B @ x km/hr  and returns @y km/hr, then his average speed during the

 

 

If  A man covers 1/3rd  of his journey at x kmph, next 1/3rd of his journey at y kmph and remaining 1/3rd journey at z kmph then his average speed during the journey = If the distance is different, then Average

 

 

Late and early cases:-

 

 

Going returning cases:- When total time is given

 

 

Boats & Streams:-
A boat is said to be moving down stream, when it is going with the stream and it is said to be moving upstream when it is going against the stream
If speed of a boat in Still water is ‘x’ kmph and speed of the stream is ‘y’ kmph then

1)speed of the boat in downstream = (x+y) kmph
1)speed of the boat in upstream = (x-y) kmph
Speed of boat in still water = ½ (downstream + upstream)
Speed of stream = ½ (downstream - upstream)

 

Theorem:-

A man rows a certain distance downstream in x hours and returns the same distance in ‘y’ hours.
If the stream flows at the rate of Z km/hr, then the speed of the man in still water is given by

 

 

Note:- Cor.(to the above theorem)

 

 

Eg: 1

A train travels a distance of 595  km in 8 ½ hours. What is its speed?
Solution:

Time taken to travel distance = 8 ½ hours = 17/2 hours
Speed of train = Distance/Time

=595/ 17/2 km/ph

=595 * 2 /17 = 70 km/ph

Speed of train is 70 km/ph

 

Eg:2

A bus travels at a speed of 45 km/hour. How far will it travel in 36 minutes?

Solution:

Speed = 45 km/hour
Time = 36 minutes
       = 36/60 Hour (Since we know, 1 hour = 60 minutes)
       = 3/5 hour
Distance = speed × time
            = 45 × (3/5) km
            = (45 × 3)/5 km
            = 27 km.

 

Eg3:- James can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 km per hour.  Find speed of James in still water:

 

 

Eg4:-In the above problem, speed of James in still water be 12 km/hr, find the speed of the strea.

 

 

 

Practice following examples

 

1)A train travels a distance of 170  km in 5 hours. What is its speed?

1)34 km/ph 2)24 km/ph 3)30 km/ph 4)32 km/ph

Ans : 34 km/ph

 

2)A train moves with the speed of 180 km/ph. Its speed (in meters per second) is ?

1)5 sec 2)40 sec 3)30 sec 4)50 sec

Ans : 50 sec

 

3)An sportsman runs 200 meters race in 24 seconds. His speed ( in km/ph)?

1)20 km/ph 2)24 km/ph 3)28.5 km/ph 4)30 km/ph

Ans : 350 km/ph

 

4)The speed of a car is 40 km/ph. What distance can it cover in 9 sec?

1)50 mts 2)120 mts 3)100 mts 4)180 mts

Ans : 100 mts

 

4)A train 250 mts long is running at 45 km/ph. In what time can it pass a pole?

1)28 sec 2)24 sec 3)36 sec 4)20 sec

Ans : 20 sec

 






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