Problems on trains:Time,Speed and Distance

Important formula

1.km/h to m/s conversion

 x km/h=(x *5/18)m/s

2.m/s to km/h conversion

X m/s=(x *18/5)km/h

Formula related to the Time,Speed and Distance

1.When two trains are going in the same direction at x m/s and y m/s,where x>y then their relative speed is (x-y)m/s.

2.When two trains are going in the opposite direction at x m/s and y m/s then their relative speed is (x-(-y))=(x+y).

3.if two trains of length x meter and y meter are going in opposite direction with the speed of  u m/s and v m/s respectively then 
Time taken by the trains  to cross each other=(x+y)/(u+v).

4.if two trains of length  x meter and y meter are going in the same direction with the speed of u m/s and v m/s respectively then

Time taken by the trains  to cross each other=(x+y)/(u-v).

5.if two trains are starting at  the same time from points A and B towards each other and they crossed at a second and b second to reach the B and A respectively. Then
(A’s speed):(B’s speed)=(root(b):root(a))

6.When train crosses the standing pole or lamp or signal post  then travelled distance would be the length of the train.

7.when train of length l meter crosses the standing man/pole/signal post of length b meter then total distance covered by the train would be (l+b) meter.  

Note:if two trains of length x meter and y meter are going either the same direction or opposite direction then distance covered by the train always be (x+y).

Solved Questions and Answers

1.A train is running at the speed of 54 km/h crosses a pole in 6 seconds.What is the length of the train ?

Solutions:
speed=54 km/h=(54*5/18)=3*5=15 m/s
time=6 seconds

Therefore,length of the train=speed * time=15 *6=90 meter

Shortcut:

Length of the train=(54 *5/18)*6=90 m

2.A train is running at the speed of 54 km/h.If the length of train is 100 meter then how long will it  take to cross 200 meter railway station ?

Solutions:
Speed of train=(54 *5/18)=15 m/s
Distance covered to cross the railway station=(100+200)=300 m
Time taken=300/15=20 second

Shortcut:

Time=(total distance)/speed=(100+200)/15=300/15=20 second

3.A train 240 meter long passes a pole in 24 seconds.How long will it take to pass a platform 650 meter long ?

Solutions:
Train speed=(240/24)=10 m/s
Therefore,Time=(Total distance)/speed=(240+650)/10=890/10=89 second

Shortcut:

Time=(total distance)/speed=(240+650)/(240/24)=890/10=89 second

4.A train is running at 72 km/h crosses another train running in the same direction at 18 km/h in 10 seconds.What is the combined length of both trains ?

Solutions:
First train speed=(72 *5/18)=20 m/s
Second train speed=(18 *5/18)=5 m/s

Relative speed=(20-5)=15 m/s (Because both trains are in same direction)

Time taken by the first train to  cross the second  train=10 seconds

Therefore,combined length of the trains=15 *10=150 meter

Shortcut:

We know that,

Relative speed=(72 *5/18)-(18 *5/18)=15 m/s
time=10 seconds
Combined length of the train=(relative speed)*time=150 * 10=150 meter

5.If a train of length 200 m is running at a speed of 20 m/s and a person is running  at a speed of 10 m/s in the opposite direction of the train.Find the time taken by the train to cross the person.

Solution:
Relative speed=(20+10)=30 m/s (Because of opposite direction)
Length of train=200 m

Time taken by train to cross the person=200/30=6.6 second

Shortcut

Time=Distance/relative speed =200/(20+10)=200/30=6.6 second

6.If A train of length 200 m is running at 36 km/h  and another train B of length 100 m is running at 18 km/h in the same direction of train B.Find out the time taken by train A to cross the train B.

Solution:
Total length of train A & B=(200+100)=300 m 
Relative speed=(36-18)=18 km/h =(18 *5/18)=5 m/s (Because of same direction)

Time taken by train A to cross train B=300/5=60 second

7.If two trains are running in opposite directions cross a standing pole in 30 seconds and 20 seconds respectively and they cross each other in 25 seconds.Find the ratio of their speeds.

Solutions:
Let speed of first train=p m/s and speed of second train=q m/s
Therefore,
length of first train=30p meter
Length of second train=20q meter
Relative speed=(p+q)m/s (Because of opposite direction)

so,Time=Distance/Relative speed

 =>25=(30p+20q)/(p+q)
=>25p+25q=30p+20q
=>25q-20q=30p-25p
=>5q=5p
=>.p=q

Therefore,p:q=1:1

8.If two trains are running in the opposite direction with the  same speed.The length of each train is 200 meter.If they cross each other in 10 seconds.Find out the speed of each train.

Solutions:

Total distance covered by the trains=(200+200)=400 meter
Time=10 seconds

Relative speed=400/10=40 m/s

Here,relative speed is total speed of the trains and both train speed same.so
Each train speed=40/2=20 m/s

9.A train passes the platform in 36 seconds and the man standing on the platform in 20 seconds.If the speed of the train is 54 km/h.What is the length of the platform ?

Solution:
Speed of the train=(54 *5/18)=15 m/s
Length of the train=(15 *20)=300 meter

Let,length of platform=x meter

Then,300+x/15=36
=>300+x=540
=>x=540-300
=>x=240 meter

Therefore,length of platform=240 meter

10.A train of length 200 meter is running at speed 144 km/h.It crosses another train running in same direction at speed 72 km/h in 10 seconds.Find out the length of other train.

Solution:
Relative speed=(144-72)=54 km/h=(144 *5/18)=40 m/s (Because of same direction)
Time=10 seconds

Distance covered by the train=40 *10=400 meter

Therefore,length of other train=(400-200)=200 meter

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