Aptitude - Problems on Trains - Discussion

10. 

A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

[A]. 3.6 sec
[B]. 18 sec
[C]. 36 sec
[D]. 72 sec

Answer: Option C

Explanation:

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.

   = 36 x 5 m/sec
18

   = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Time taken = 360 sec = 36 sec.
10

Karthik said: (Jun 6, 2010)  
Y DID U substract 45-9? i didn't understand

Rprabha said: (Jun 10, 2010)  
If in both the objects move in the same direction, the relative speed would be the sum of both the speeds. How is calculation is done. Even if tried with the mentioned procedure, the options don't have the derived answer

Ramesh Karthick said: (Jun 16, 2010)  
Jogger is not idle. He also running. So we done this step 45-9km/hr.

9km/hr is jogger speed.

Karthik said: (Jun 30, 2010)  
Relative speed= hidh speed + low speed when the objects are moving in the oppsite direction
Relative speed= hidh speed - low speed when the objects are moving in the same direction

Sarika said: (Aug 16, 2010)  
Yes, karthik is right.

Chetan said: (Aug 26, 2010)  
Relative speed means speed of an object w.r.t to another object.

Tips:

1.)Two objects moving in same direction-->stop object 2 and subtract object 2' s speed from object 1.

Ex: Suppose two cars moving in same direction with 60 kmph(both cars same speed)..it is obvious that relative speed is 0 kmph....how did it come??? by subtracting..ok.

2.) Two objects moving in oppsite direction--->stop obj 2 and add its speed to obj1.

Ex:
Car1 speed=40 kmph in east direction.
Car2 speed=50 kmph in west direction.
Relative speed of car1 w.r.t car2 is
stop car2, add its speed to car1, i.e 40+50 = 90.

Priyanka said: (Sep 23, 2010)  
Can you explain me why in this question relative speed is subtaction of higher speed to lower while in same direction relative speed is addition of both object speed?

Jelli said: (Dec 11, 2010)  
Hi
i think you can use the formula

u=(a+b)/(u-v) (both in a same dir)
=(120+240)/(45-9)*5/18
=36s

Sumi said: (Dec 17, 2010)  
hi priyanka u understood wrongly relative speed for the objects in same direction is obtained by subtracting only

Dheeraj said: (Jun 16, 2011)  
@rprabha... no when two things are going in same direction then realtive speed is not sum of that things..

Gayathri said: (Jun 22, 2011)  
Logic 1
Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.

Here the train moves at 45 km/hr and the jogger moves at 9 km/hr in same direction... relative speed = (45-9)= 36 km/hr and since the distance is in meters we have to convert the relative speed i.e 36 km/hr to meter/sec by multiplying 5/18.

therefore, relative speed = 36 * 5/18 = 10 m/sec

Logic 2
If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:

The time taken by the faster train to cross the slower train = (a + b)/(u-v).

In this question the train moves 120 m and jogger moves 240 m
total distance = 120 + 240 = 360

now we know relative speed and distance, so we can easily compute time by applying the formula time = distance / speed

time = 360 / 10 = 36 secs

Hope u understood friends

Viji said: (Jul 31, 2011)  
Any body please explain that the relative speed calculation for both speed and distance when opposite and same direction moving ?

Harika said: (Aug 16, 2011)  
When we have to calculate relative speed?

Viji.T said: (Aug 28, 2011)  
The distance taken here is not clear for me. They use the term ahead of the engine like that. What they mean there. To take a distance as (120+240) , what is the logic behind that. Please can anyone explain me?

Deepak Agrawal said: (Sep 5, 2011)  
@Harika
we calculate the ralative speed when two object are run simultenously in parallel .

Aditya Bala said: (Oct 12, 2011)  
We calculate relative speed for opposite and same direction if they travel in opposite direction we add them, in same direction we substract them.

M.V.Rama Krishna Kumar Reddy said: (Nov 12, 2011)  
For the same direction we get relative speed by subtracting speeds.

Partha said: (Nov 16, 2011)  
@Viji.T
i agree with u .. by the time the train approaches the jogger he/she would have covered some additional distance...how is that even possible to take the sum (240+120) as the total distance travelled ignoring the the distance covered by the jogger in that time interval...

Anushka said: (Feb 17, 2012)  
Ya gayatri I agree with you.

Shaina said: (Jun 2, 2012)  
What is kmph?

Kradeep Khera said: (Jun 4, 2012)  
kmph=kilo meter per hour or km/hr

Gaurav Choubey said: (Jul 22, 2012)  
Step 1 find train speed in m/s 45*5/18=10m/sec.

Length og train=speed*time.

120=10*x=12 sec.

But 240 more to covered then

240+120=10*x.

x=36 answer.

Manish Kumar Meena said: (Aug 25, 2012)  
How can the distance be 240 + 120. Until the train's engine covers 240m in that time the jogger will also move some distance ahead. So the total distance is not 240+120.

Md Ashique said: (Oct 2, 2012)  
@Manish kumar mina.

Yeah you are right. We are not finding the time w.r.t platform, its w.r.t the man, who is moving with 9kmph, so the total distance will be 120+0=120 and required time will be (120+0) / (45-9) =12 sec.

Dhanu said: (Jan 9, 2013)  
The total distance covered by the train when it passes by the jogger should be (120+240+distance covered by jogger during that time say "x") right?

So it will be
x = 9*(5/18)*T, where T is our required answer.
i.e x = 5/2*T m

And according to given details,

Relative speed = (45 - 9) km/hr = 36 km/hr.
i.e 10m/sec

T = ((120+240+x)/10 )seconds

Putting value of x = 5/2*T

T = ((120+240+(5/2)*T)/10 )
= ((360+(5/2)*T)/10 )

i.e

10*T = 360+2.5*T
7.5*T = 360
T = 48 seconds.

This should be also correct right?

Biswajit said: (Apr 1, 2013)  
Dhanu,

You are right. As the jogger is also in motion so its speed should be considered and that changes the time significantly. I wonder why no one have pointed this earlier.

Maulik Dodia said: (Jul 1, 2013)  
But I can not understand, that the tain have to pass the only 120m distance w.r.t the jogger. Not 240? Isn't it? Can anyone explain me that?

Amresh said: (Aug 15, 2013)  
Total distance should be= 120+240+x.

Raju Pathro said: (Aug 21, 2013)  
We can add jogger length also but it is neglected when compare with train.

Neel said: (Aug 31, 2013)  
We subtract 45-9 so as to make the position of the jogger to be the reference position. By subtracting that the jogger is stationary now.

Neel said: (Aug 31, 2013)  
Thus now the total distance covered by train is 240+120 only.

Jay said: (Sep 12, 2013)  
Relative speed concept when two object moves in same direction than their speed is equal to the subtraction of their actual speed. Relative speed is a speed of one object with respect to another ok.

Prerna said: (Nov 30, 2013)  
Do we suppose to pass the platform too. If jogger is also moving there is no point in considering the jogging track length.

Relative speed is 10 m/s hence to pass the train of length 120m we will need only 12 sec.

Preethi said: (Jan 26, 2014)  
@Dhanu: Initially when I read the question I also followed your concept. But relative speed is a different concept. When you are considering relative speed the distance traveled by the jogger is also considered hence only the initial distance which has to be traveled alone is enough to calculate the time required. Where as when you do chocolate method I mean work and time problem you can apply the concept.

Hari said: (Jul 24, 2014)  
You asked the question for cross the jogger only, but you calculate for the platform, please give me the explanation.

Saurav said: (Aug 2, 2014)  
Relative speed itself means that the speed of other object is 0. As we are finding the speed of the train relative to man. (45-9 = 36). So man has been made to be in rest.

Vedant said: (Aug 31, 2014)  
@People considering distance traveled by jogger.

240 + 120 + 9*A (5/18) / (45*5/18) = A.

This will give A=36 so given solution is correct do no take relative speed concept just simply add distance to be covered and divide by train speed.

Ramsha said: (Sep 30, 2014)  
Yes @Vedant, I also get the same answer through the same process.

Atoria M. Horace said: (Nov 8, 2014)  
I still can't understand how the 5/18 came about.

Prashant said: (Dec 18, 2014)  
Please clear my doubt.

Let the train pass after t time.

So train has to cover (120+240+x)/45 in t time.

And jogger covers x/9 in t time.

(120+240+x) /45 = x/9.

Answer is 90 sec but logic is correct that they both meet after t time.

Ram said: (Jan 15, 2015)  
Answer is 48 sec as jogger also jogs 2.5x distance.

= 360+2.5x/x = 10.

= 360+2.5x = 10x.

= 360 = 7.5x.

= 48 = x.

Hence 48 sec is the answer.

Padma said: (Jan 31, 2015)  
Question asked about at what time train cross man. Man has no length then why we add track length?

Monica said: (Feb 3, 2015)  
Why we add track length means because man is running on track? So man gets the track length.

Sushanto said: (Feb 11, 2015)  
Why (36 x 5/18) is used? How you get 5/18?

Ankush said: (Apr 8, 2015)  
5/18 we can get like that.

Suppose speed is 10 km/hr so we can say like that.

(10)*1000/3600 m/second, so 1000/3600 will become 5/18.

Raji said: (Apr 27, 2015)  
What is the difference between 2nd problem and 10th problem?

Ishan said: (May 14, 2015)  
"A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine" - This means The engine is 240 metres behind of that person. So the train has to cover that distance (120+240) metres by it's own speed (without considering relative speed as it has not reached that jogger yet) and after that train has to cover that jogger (considering relative speed).

When the train is covering (120+240) metres the jogger has moved some extra distance in forward direction by that time. So thinking in that way is going to be more complex.

Here we have to think of two moving objects - one is the train which is of length 120 metres and of speed 45Kmph. Another is of length 240 metres and of speed 9Kmph in Same Direction. (Like two trains moving in same direction with different speed).

So, total length = 240+120 = 360 metres.

Relative speed = (45-9) Kmph = 36*(5/18) m/s = 10m/s.

Hence time = 360/10 = 36 seconds.

Aaditya said: (Jun 9, 2015)  
For the 1st 240m. Why are calculating the relative speed?

The jogger comes alongside the train after 240m. So, after that the relative speed should be considered. Please explain.

Rohit Basuri said: (Jul 4, 2015)  
The jogger is also running. So, we also need to factor in the additional distance he covers.

If the time taken by train to cross the jogger is x.

(360+(9*5/18)*x)/10 = x.

x = 48 sec.

Nilesh said: (Jul 28, 2015)  
t = a+b/u-v.

Manojbatchu said: (Aug 24, 2015)  
In how much time train crosses the jogger?

Then why they are adding the 240 m railway track length?

Jogger speed, train speed, train length enough. Please any one solve my doubt.

Rahul said: (Sep 27, 2015)  
The jogger is not idle eight, I think it is wrong because the jogger will run at a speed of 9 kmph during the time the train passes him so this distance should also be covered I solution but it is not the answer would be 48 sec.

Shubham Singh said: (Oct 3, 2015)  
Suppose jogger is running at 18 kmph and rest things are same so according to the calculation as done in explanation time should be 360/(15/2) = 48 sec but in that time jogger have also run 48*5 = 240 m so yet 120 m ahead of train.

Prakash said: (Nov 24, 2015)  
How 5/18 will came? Please clarify.

Suriya said: (Nov 27, 2015)  
In any problem we will need to keep all the values in an uniform form, i.e. either all must be in m/sec or KM\hr.

In this problem they have converted from Km\Hr to m/sec. Therefore we multiply it my 1000/3600 (1 km = 1000 meters and 1 hour = 3600 seconds). When we cancel numerator and denominator we get, 5/18. This is how we get 5/18. Hope it helps.

Reddy said: (Jan 5, 2016)  
In this problem the question is how much time it take to cross the jogger why are you considering the plat form length?

Sailesh said: (May 17, 2016)  
They asked how much time the train pass jogger. Should the entire train pass the jogger (then distance=240 + 120) or should the engine only just pass the jogger (then distance =240).

Niveditha said: (May 22, 2016)  
It's better to use shortcut method.

t = a + b /u - v.

Naveen said: (Jul 7, 2016)  
@Sailesh, What you said is correct.

Ayush Chawla said: (Jul 21, 2016)  
Could the answer be wrong? Because, according to answer jogger is idle, as the distance covered by the jogger is not considered in the total answer? According to me, 48sec should be the right answer.

Could anyone give it a thought? That total distance should be 240 + 120 + T * 9 * (5/18) , supposing x is a distance moved by a jogger. Therefore x = T * (9 * 5/18).

Then the answer is 48, which is not mentioned in options.

Sandeep said: (Jul 23, 2016)  
Can anyone explain by using formula a + b / u - v?

Priya said: (Aug 7, 2016)  
What is the unit digit of 991^45? Can anyone tell me?

Raaj said: (Nov 7, 2016)  
If the direction of both things is in the same direction then the relative speed will be subtracted but in the case of opposite direction, relative speed will be added.

Shubh said: (Dec 5, 2016)  
What will be the shortcut method if trains are moving in opposite directions?

Shubham said: (Jan 10, 2017)  
as (a+b/u-v).
(45-9) * 5/18 = 10m/s.
(120 + 240/10) = 36s.

Raj Vora said: (Jan 19, 2017)  
Can you please explain why we have to add 240 + 120?

Neerja said: (Mar 5, 2017)  
@Raj Vora.

The distance between the jogger and train is 240m so to first catch up to the jogger the train has to travel 240m. The length of the train is 120m so to completely pass the man and overtake him the train has to travel the length of the train, i.e. 120m.

Therefore total distance to be travelled by the train is 120m+240m=360m.

Hope this helped.

Shubhankar said: (Jul 1, 2017)  
Jogger is also moving, I don't think answer is correct please update we have to first come to a meeting point of train and the jogger.

Adarsh said: (Aug 15, 2017)  
Relative speed can be used only when the jogger covers 240 m in the said time. But he already is 240 m ahead of the train. Jogger is also moving, so he might also cover some distance, we have to calculate his distance. And we have to add that distance x +240 m + 120 meter. We have no idea about this distance x right?

Mohit Tiwari said: (Aug 31, 2017)  
The relative speed is 10m/s. But train needs to cover 240+2*(length of train) to pass the jogger so the answer should be 48 m/s.

Kittu said: (Sep 12, 2017)  
@Ishan.

You explained very clearly! thank you.

Abhinand said: (Dec 10, 2017)  
I think the platfr0m length n0 need t0 take. The train thake 8 sec t0 pass the man. After concider the relative speed.

120/ (36*5/18).

Neelesh said: (Feb 3, 2018)  
This question asks "In how much time will the train pass the jogger".

Here, this rule is wrongly applied in the explanation: "Distance to be covered" = 240 + 120 m (i.e. "train length" and the distance between "jogger and engine".).

As Per the question, the "Distance to be covered" should be 120 m (i.e Train length).

It doesn't make sense why this explanation is wrongly taking into consideration 240m i.e. "Distance between Train engine and Jogger"?

Satish said: (Feb 28, 2018)  
@All.

Hi, I think the question is incorrect because if they are going in the same direction then train already ahead and has high speed than jogger so the train will go away.

Sarang said: (May 4, 2018)  
Distance= speed * time.
120+240=45-9km/h*time,
360=36km/h*time,
360=36*5/18*time,
360=2*5*time,
360=10*time,
Time=360/10,
Time=36s.

Shoyeb said: (May 29, 2018)  
What about the extra distance Jogger has travelled in those 36 seconds?

Mayur said: (Jul 21, 2018)  
Why we are considering full length of the platform as 240m?

It is very much possible that the train will cross the jogger before the platform (240m) is fully covered.

Then why total distance= 120m+240m?

Gokul said: (Jul 24, 2018)  
Here the equation is (l1+l2)/(v2+v1).

Pratik said: (Jul 27, 2018)  
@All.

I have a doubt. The jogger was not static. This means he/she must have covered some distance before the train crosses, all the solutions have not included this issue. Should I neglect that distance or is there anything I am missing.

To me, total distance = train length+ 240 metre+ the joggers covered path.

Is that correct or not. If not please help.

Shubhangi Nema said: (Aug 10, 2018)  
A jogger is a point object so why we consider the platform length?

Vivek Manve said: (Aug 20, 2018)  
Jogger is also running. So he will cover some distance, that should be taken in calculation right?

Afreen said: (Aug 24, 2018)  
For same direction,

t=l1+l2/s1-s2.

Jime said: (Sep 27, 2018)  
Why do we add the distance with direction?

Mastermind said: (Dec 2, 2018)  
Same direction,

d1+d2=240+120,
d=360,

speed :(same direction,)
s1-s2=45-9=36kmph.

36*5/18=10m/s,
therefore,
assume time=x,
d=speed*time ,
360=10*(x).
36 = x.

Kavya said: (Jan 6, 2019)  
Why didn't we use relative speed formula here instead why we did use the speed of train relative to jogger?

Please explain me.

Karthik said: (Feb 17, 2019)  
Why relative speed covered entire distance. I suspect that when train engine enter to jogger after that we should consider relative speed?

Please explain anyone.

Rohan said: (Jul 23, 2019)  
Why is the total distance taken as 240+120?

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