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m

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mIn the discussion till now (as in the diginotes of the Speed Time and

Distance); we never included the length of the moving object in the

distance covered. The problem based on trains is a special case of

speed time and distance in which the length of the moving objects

becomes the distance covered. How we would be able to identify

whether the length of the moving objects should considered as the

distance covered? It will be told by the “Time of Crossing”. That will

tell us whether we should consider the length of the moving object as

distance or not as illustrated with the help of the following discussion.

IMPORTANT QUESTIONS

1. A train running at the speed of 60 km/hr. crosses a pole in 9

seconds. What is the length of the train?

Introduction:

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mmL

ssmL

STD

150

9/ 18

560

2. A train 125 m long passes a man, running at 5 km/hr. in the

same direction in which the train is going, in 10 seconds. Find

the speed of the train.

./ 50

10/ 18

55125

hrkmS

ssmSm

STD

Train

Train

3. Find the length of the bridge, which a train 130 meters long and

travelling at 45 km/hr. can cross in 30 seconds.

mL

ssmL

STD

245

30/18

545130

4. Two trains running in opposite directions cross a man standing

on the platform in 27 seconds and 17 seconds respectively and

they cross each other in 23 seconds. Find the ratio of their

speeds.

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23

46

64

23231727

23

1727

1727

21

21

21

2121

1111

2211

2211

222111

::SS

::SS

SS

SSSS

sSSLL

ST D

SLSL

sSLs SL

TS DTS D

5. A train passes a station platform in 36 seconds and a man

standing on the platform in 20 seconds. If the speed of the train

is 54 km/hr., what is the length of the platform?

mL

mLm

s m/sLL

ST D

Now

mL

sm/sL

STD

P

P

PT

T

T

240

540300

3618

554

300

2018

554

6. A train 240 m long passes a pole in 24 seconds. How long will it

take to pass a platform 650 m long?

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msT

Tm/smmm/s S

TSLLs Sm

ST DST D

T

TPTT

89

1065024010

24240

7. Two trains of equal length are running on parallel lines in the

same direction at 46 km/hr. and 36 km/hr. The faster train

passes the slower train in 36 seconds. Find the length of each

train.

50

3618

53646

L

sLL

STD

8. A train 360 m long is running at a speed of 45 km/hr. In what

time will it pass a bridge 140 m long?

sT

Tsmm

STD

40

/18

545140360

9. Two trains are moving in opposite directions @ 60 km/hr. and 90

km/hr. Their lengths are 1.10 km and 0.9 km respectively. Find

the time taken by the slower train to cross the faster train.

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m

sT

Tsmm

STD

48

/18

560909001100

10. A jogger running at 9 kmph alongside a railway track in 240

meters ahead of the engine of a 120 meters long train running at

45 mph in the same direction. In how much time will the train

pass the jogger?

sT

Tsmm

STD

36

/18

5945240120

11. A 270 meters long train running at the speed of 120 kmph

crosses another train running in opposite direction at the speed

of 80 kmph in 9 seconds. What is the length of the other train?

mL

ssmmL

STD

230

9/18

580120270

12. A goods train runs at the speed of 72 kmph and crosses a

250 m long platform in 26 seconds. What is the length of the

goods train?

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m

mL

ssmmL

STD

Train

Train

270

26/18

572250

13. Two trains, each 100 m long, moving in opposite directions,

cross each other in 8 seconds. If one is moving twice as fast the

other, then find the speed of the faster train.

km/hrStrainhe faster Speed of t

km/hrS

sm/sSSm

ST D

603022

30

818

52100100

14. Two trains 140 m and 160 m long run at the speed of 60

km/hr. and 40 km/hr. respectively in opposite directions on

parallel tracks. Find the time (in seconds) takenin which they will

cross each other.

sT

Tsmmm

STD

8.10

/18

54060160140

15. A train 110 meters long is running with a speed of 60 kmph.

In what time will it pass a man who is running at 6 kmph in the

direction opposite to that in which the train is going?

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sT

Tsmm

STD

6

/18

5660110

16. A train travelling at a speed of 75 mph enters a tunnel

3𝟏 𝟐⁄ miles long. The train is 𝟏

𝟒 miles long. How long does it take

for the train to pass through the tunnel from the moment the

front enters to the moment the rear emerges?

.min36075

1

4

33

/752

13

4

1

sT

Thrmilesmiles

STD

17. A train 800 meters long is running at a speed of 78 km/hr.

If it crosses a tunnel in 1 minute, then find the length of the

tunnel (in meters).

mL

ssmmL

STD

Tunnel

Tunnel

500

60/18

578800

18. A 300 metre long train crosses a platform in 39 seconds

while it crosses a signal pole in 18 seconds. What is the length of

the platform?

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m

mL

sm/smL

STD

Again

m/s S

sSm

ST D

Platforml

Platforml

Train

Train

350

393

50300

3

50

18300

19. A train speeds past a pole in 15 seconds and a platform 100

m long in 25 seconds. Find Its length.

sSmL

STD

Again

s SL

ST D

TrainTrain

TrainTrain

25100

15

20. A train moves past a telegraph post and a bridge 264 m

long in 8 seconds and 20 seconds respectively. What is the speed

of the train?

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m

smS

sSmS

sSmL

STD

Again

SsSL

ST D

Train

TrainTrain

TrainTrain

TrainTrainTrain

/ 2212

264

202648

20264

88

21. How many seconds will a 500 metre long train take to cross

a man walking with a speed of 3 km/hr. in the direction of the

moving train if the speed of the train is 63 km/hr.?

sT

Tsmm

ST D

30

/18

5363500

22. Two goods train each 500 m long, are running in opposite

directions on parallel tracks. Their speeds are 45 km/hr. and 30

km/hr. respectively. Find the time taken by the slower train to

pass the driver of the faster one.

sT

Tsmm

ST D

24

/18

53045500

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m23. Two trains are running in opposite directions with the

same speed. If the length of each train is 120 meters and they

cross each other in 12 seconds, then find the speed of each train

(in km/hr.).

hrkmsmS

sSSm

ST D

/365

1810/10

12120120

24. Two trains of equal lengths take 10 seconds and 15 seconds

respectively to cross a telegraph post. If the length of each train

be 120 meters, in what time (in seconds) will they cross each

other travelling in opposite direction?

sT

Tm/sm

ST D

Again

m/sSm/s S

s Ss S

ST DST D

12

812120120

812

1512010120

21

21

25. A train 108 m long moving at a speed of 50 km/hr. crosses

a train 112 m long coming from opposite direction in 6

seconds.Find the speed of the second train.

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hrkmsmS

sSSm

ST D

/365

1810/10

12120120

26. Two trains are running at 40 km/hr. and 20 km/hr.

respectively in the same direction. Fast train completely passes a

man sitting in the slower train in 5 seconds. What is the length

of the fast train?

sL

ssmL

ST D

Faster

Faster

9

727

9

250

5/18

52040

27. A train overtakes two persons who are walking in the same

direction in which the train is going, at the rate of 2 kmph and 4

kmph and passes them completely in 9 and 10 seconds

respectively. Find the length of the train.

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m

mL

L

sSL

Hence

smS

sSsS

Now

s SLs SL

STDST D

Train

Train

TrainTrain

Train

TrainTrain

TrainTrainTrainTrain

180

9222

92

/22

10492

10492

28. A train overtakes two persons walking along a railway

track. The first one walks at 4.5 km/hr. The other one walks at

5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to

overtake them. What is the speed of the train if both the

persons are walking in the same direction as the train?

hrkmS

ssmSssmS

Now

s smSLs smSL

STDST D

Train

TrainTrain

TrainTrainTrainTrain

/81

5.8/18

54.54.8/

18

55.4

5.8/18

54.5 4.8/

18

55.4

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m29. A train travelling at 48 kmph completely crosses another

train having half its length and travelling in opposite direction at

42 kmph, in 12 seconds. It also passes a railway platform in 45

seconds. Find the length of the platform.

mL

sm/sLL

ST D

Again

m L

s m/sLL

ST D

Platform

Platform

400

4518

548

200

1218

54248

2

1

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NOTES