Aptitude - Problems on Trains - Discussion

In this question, we have been asked to find the time taken by the train to pass the jogger when it is given that the jogger’s speed is 9 kmph and the train’s speed is 45 kmph and the jogger is 240 m ahead of a 120 m long train. To solve this question, we should know about relative speed, which is the speed of one object with respect to the other and when both objects are moving in the same direction, then their difference is taken as their relative speed. So, we can say that the relative speed of the train with respect to the jogger is, the speed of the train - speed of the jogger.

So, we get,

Relative speed of train = (45 - 9)kmph = 36 kmph.

So, if we consider the relative speed of the train as the original speed, then we have to assume that the jogger is standing. So, we can say that the train must travel a distance of (240 + 120) m = 360 m as the front of the engine and the jogger are 240 m apart and the engine is 120 m long.

Now, we know that 1 km = 1000 m and 1 hr = 3600 sec. So, we can say that, 36 kmph = 36×10003600=10.

Mpsec.

We know that speed, distance, and time are related as, speed=distancetime.
It can also be written as, time=distancespeed.
Now, we know that the train has to travel 360 m with a speed of 10 mpsec. So, we can say that,
Time taken = 36010⇒36sec.
Hence, we can say that a 120 m long train with a speed of 45 kmph at a distance of 240 m from a jogger who is running at a speed of 9 kmph will cross the jogger in 36 sec.
Therefore, the correct option is option C.

"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.

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

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.

When the train is moving towards the jogger the jogger is still running at 9Kmph or 2.5 m/sec so by the time the engine reaches 240mtrs the jogger would've moved forward.

Time taken for front of train to cover 240 mtrs = 24 secs (time = distance / speed{relative = 10 m/s})

Also the distance travelled by jogger in this 24 secs is = 2.5 mtr/sec * 24 sec = 60 mtrs
so in order for the train to completely pass the jogger, it has to travel 60 mtrs more.

Total distance = 60 + 120 = 180 m.
Speed = 10 m/s.
Time = 18 sec.

Total time = 18 + 24 = 42 sec.

Is this method is correct?

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?

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"?

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.

@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.

I also agree with you @Ravi by the time when the train takes 36 sec to cross the jogger. The jogger also traveled some dist at that 36 sec of time. Jogger speed is 9km/hr which is 2. 5m/sec which means joggers must have covered 2. 5x36=90 m of dist that's mean now the train has to cover 90 m more to actually cross that jogger.

Am I correct? Please anyone explain me.