Time and Distances - 3

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Time and Distances

Problems on Trains

1. A train crosses a pole in 12 sec. It crosses a bridge of length 300m in 27sec. what is the time taken by the train to cross a bridge of length of 600m?

2. A train crosses a bridge of length 122m in 17 sec. it crossed another bridgeof length 210m in 25 sec. find the length of the train?

3. A train travelling at a speed of 54kmph crosses a platform in 36 sec and aman standing on the platform in 20 sec. find the length of the platform?

4. A train of length 240m travelling at a speed of 64kmph overtakes a manrunning at a speed of 10 kmph in __ sec ?

5. A train starts from a station X at 6am and reaches another station Y at 10am. Another train starts from station Y at 8am and reaches station ‘X’ at11:30am. At what time do the trains cross each other?

A train crosses a pole in 12 sec. It crosses a bridge of length 300m in 27 sec.what is the time taken by the train to cross a bridge of length of 600m?

Ans :NOTE:• To cross a pole, A train has to travel a distance equal to length of train.• To cross a bridge, A train has to travel a distance equal to length of train +

length of the bridge.

12 12 15 12 ?(30)Time taken by the train to cross a bridge of length of 600m = 42sec

1.

Time taken by the train to cross a bridge of length of 600m = 42sec

300 – 15600 – 30

A train crosses a bridge of length 122m in 17 sec. it crossed anotherbridge of length 210m in 25 sec. find the length of the train?

2.Ans :NOTE:• To cross a pole, A train has to travel a distance equal to length of train.• To cross a bridge, A train has to travel a distance equal to length of train +

length of the bridge.

? x 17-x x 25-x 8 sec – 88m 17 sec - ? (187m) Length of the train = 187 – 122 = 65m

300 – 15600 – 30

Length of the train = 65m

A train travelling at a speed of 54kmph crosses a platform in 36 sec and aman standing on the platform in 20 sec. find the length of the platform?

3.

Ans :

20 20 16 Length of the platform = 15*16 = 240m

Length of the platform = 240m

54kmph– 15m/sec

Relative speed: Speed of the body W.R.T to another body• If 2 bodies A and B are travelling at speeds of ‘x’ kmph and ‘y’ kmph

respectively• In opposite direction:

Speed of A W.R.T to B = x + y kmph• In same direction :

Speed of A W.R.T to B = x - y kmph• If 2 trains of lengths and are travelling at a speed of and respectively

• In opposite direction:Time taken by two trains to cross each other =

kmph• In same direction :

Time taken by two trains to cross each other = kmph (if )

A train of length 240m travelling at a speed of 64kmph overtakes a manrunning at a speed of 10 kmph in __ sec ?

4.

Time taken by the train = 16 sec

Ans :Train and man are running in the same direction Relative speed = 64 – 10 = 54kmph = 15m/sec Time taken by the train = = 16 sec

54kmph– 15m/sec

A train starts from a station X at 6am and reaches another station Y at10 am. Another train starts from station Y at 8am and reaches station‘X’ at 11:30am. At what time do the trains cross each other?

5.

Ans := 4 hrs, = 3 ½ hrs : = 4 : = 8 : 7

: = 7 : 8Assume d = 8 7 = 56km( d = s t)

=> = 56/4 = 14kmph = 56/3.5 = 16kmphRelative speed = 14 +16 = 30kmphBy 8:00 am the 1st train reaches half of the distance and2nd train has yet to start

28 286 10

11:30 8

8

Relative speed = 30kmph=> 30 km – 1hr

28 km - ? (56min)=> In the second half journey after 56 min the trains willcross each other i.e. 8:56am.

30 – 60min28 – 56min

Trains will cross each other at 8:56am.

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Problems for practice are given in the description of the video.

Practice problemson Trains

Two trains of equal length cross a pole in 4 sec and 5sec respectively. Whatis the time taken by the two trains to cross each other travelling in oppositedirection?Two trains of lengths 225m and 275m respectively travelling in oppositedirection cross each other in 10 sec. If they travel in the same direction, thenthe faster train over takes the slower train in 50 sec. find the speed of thefaster train?A train starts from a station X at 8am and reaches another station Y at 10:30am. Another train starts from station Y at 8:15am and reaches station ‘X’ at10:15am. At what time do the trains cross each other?A train of length 240m travelling at a speed of 64kmph overtakes a manrunning at a speed of 10 kmph in __ sec ?

1.

2.

4.

3.

Two trains of equal length cross a pole in 4 sec and 5sec respectively.What is the time taken by the two trains to cross each other travelling inopposite direction?

1.

The time taken by the two trains to cross each other = 40/9 sec

Let the length of the train == , = =

Time taken in opposite = = = sec

Ans :

Two trains of lengths 225m and 275m respectively travelling in oppositedirection cross each other in 10 sec. If they travel in the same direction,then the faster train over takes the slower train in 50 sec. find the speedof the faster train?

2.

speed of the faster train = 30 m/sec

= 225m = 275m Speed in opposite = = 50m/sec = + Speed in same direction = = 10m/sec = - = 30 m/sec = 20 m/sec

Ans :

A train starts from a station X at 8am and reaches another station Y at10:30 am. Another train starts from station Y at 8:15am and reachesstation ‘X’ at 10:15am. At what time do the trains cross each other?

3.

Ans := 2 ½ hrs, = 2 hrs : = : 2 = 5 : 4

: = 4 : 5Assume d = 4 5 = 20km( d = s t)

=> = 20/2.5 = 8kmph = 20/2= 10kmphRelative speed = 8 +10 = 18kmphBy 8:15 am the 1st train reaches 2km of the distance and2nd train has yet to start

2 188 10:30

10:15 8:15

A train of length 220m travelling at a speed of 60kmph will cross a manrunning at a speed of 12 kmph in opposite direction in __ sec ?

4.

Time taken by the train to over take the man = 11 sec

Ans :Train and man are running in the opposite direction Relative speed = 60 + 12 = 72kmph = 20m/sec Time taken by the train = = 11 sec

72kmph– 20m/sec

Relative speed = 18kmph=> 18 km – 1hr

=> In the second half journey after 1 hr the trains willcross each other i.e. 9:15am.

Trains will cross each other at 9:15am.

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