M11-03

Question

If a passenger seated by the window on a train moving at 40 km/h observed that an oncoming train took 3 seconds to pass him, how fast was the oncoming train moving if it was 75 meters long?

A. 50 kmh
B. 52 kmh
C. 56 kmh
D. 60 kmh
E. 70 kmh

Bunuel · Accepted Answer

Official Solution:

If a passenger seated by the window on a train moving at 40 km/h observed that an oncoming train took 3 seconds to pass him, how fast was the oncoming train moving if it was 75 meters long?

A. 50 kmh
B. 52 kmh
C. 56 kmh
D. 60 kmh
E. 70 kmh

Let's represent the speed of the oncoming train as  v . Relative to the passenger, its speed would be  v + 40  km/h. If it covers 75 meters in 3 seconds, that's equivalent to 25 meters in 1 second. This speed is equal to  \frac{25 * 3,600}{1,000} = 90  km/h (multiplying by 3,600 to get speed in hours and dividing by 1,000 to convert meters into kilometers). Therefore,  v + 40 = 90 , which gives  v = 50  km/h.

Answer: A

Mahmud6 · Answer

"Then its speed relative to the passenger is  V + 40 ." ----> Could not understand it. Would you please clarify this a little bit.

Bunuel · Answer

This is the concept of Relative Speed.

When two objects (speeds V1 and V2) move in opposite directions (towards each other or away from each other), they cover the distance between them (or create distance between them) at the rate of (V1 + V2).

When two objects move in same direction, their speeds get subtracted.

Theory on Distance/Rate Problems: https://gmatclub.com/forum/distance-spe ... 87481.html

All DS Distance/Rate Problems to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=44
All PS Distance/Rate Problems to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=64

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

Sakshi15 · Answer

I still did not get this part:

V+40=90V

WHY IS IT SO?

ArnoldPushkin · Answer

Maybe my reply is outdated to you, but it could be relevant for those who face this question in the future.
Firstly, to understand this question and the solution you need to be good with the concept of relative speed.
What is relative speed? Basically, it is speed of an object relative to another object. For example- Person A is standing still and B is moving at a speed of 5 mph. What is their relative speed to each other? That is right, 5 mph! But if they started to move to opposite directions: A moves at 2 mph and B at 5 mph in opposite directions, they moving away from each other at 7 mph, therefore they relative speed is 7 mph. If they started to move toward each other: A at 2 mph, and B at 5 mph, they are still covering 7 mph. If they are moving in the same direction, say, A at 2 mph and B at 5 mph, they relative speed to each other is 3 mph. Hope it makes sense.
Back to your question, this equation is basically=(unknown speed at kmph)+(known speed at kmph)=(relative speed toward each other at kmph)
Hope it helps

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

BongBideshini · Answer

Bunuel , how are you inferring that both trains are in opposite directions?

Bunuel · Answer

The direction is inferred from the word  oncoming  in the question.  Oncoming train  means the other train is approaching from the opposite direction, not traveling in the same direction.

isteducimus · Answer

however, in case of speed of stream and boat, we add when downstream (same direction) and subtract when upstream (opposite directions), right?

Bunuel · Answer

Yes, but notice the difference.

In boat–stream problems, the boat already has its own speed in still water. The stream either adds to it when downstream (same direction) or reduces it when upstream (opposite directions).

In two-trains problems, you are comparing the motion of two independent objects.
 
If they move toward each other in opposite directions, the relative speed is the sum of the two.
If they move in the same direction, the relative speed is the difference of the two.

So both follow the same principle of relative speed. Whether you add or subtract depends only on whether the motions are in the same direction or in opposite directions. In the boat–stream case, the stream is not an independent object but rather modifies the boat’s net speed.

Anish27 · Answer

Time Taken = Distance / Relative speed
3 sec = 1/1200 hr
75 m = 3/40 Km
Since it is opposite direction, we have to add relative speed, x+40
1/1200 = 3/40/x+40
1/1200 = 3/40 * 1/x+40
40x =2000
x =50 km/hr

f3rn4nd44m0r1m · Answer

I like the solution - it’s helpful.

AbhishekP220108 · Answer

We can solve this problem by relative speed concept, since it was given both trains are moving in opp direction and crossed the seating person in 3 sec and the distance of oncoming train is 75 meter, so we can also infer that the meeting time when the distance is 75mtr is 3 sec so substitute the value after converting to km and hr in time to meet for relative speed i.e Tmeet=dist/sum of speeds, sum because the two trains are in opp direction

Bunuel

If a passenger seated by the window on a train moving at 40 km/h observed that an oncoming train took 3 seconds to pass him, how fast was the oncoming train moving if it was 75 meters long?

A. 50 kmh
B. 52 kmh
C. 56 kmh
D. 60 kmh
E. 70 kmh

dignissimosminima · Answer

A good way to get a better understanding of relative speed is to think "If i were sitting on a train, a train coming towards me would seem to cross faster than its actually moving." And consecutively, "If I were sitting on a train a train overtaking me would feel moving at a speed slower than its actually moving." Basically you fix a point of reference and (in this case, you and the train you are on) and evaluate the speed of the other object. It is important to consider the directions of the movements as well.

M11-03

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