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mangamma
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 19 Apr 2019, 09:07
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A train 500 metres long is crossing a tunnel 5 kilometres long at a speed of 30 kilometres per hour. What is the difference in the time in minutes for which all the passengers of the train are inside the tunnel and the time for which a particular passenger is inside the tunnel?

A. 1
B. 1.5
C. 2
D. 3
E. 5
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A
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GMATaspirant641
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 24 Apr 2019, 20:59
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effatara

I came up with the same answer but with a different logic.

1) The Time that one passenger is inside the tunnel = time taken by that one passenger to cross the tunnel = 5/30 = 1/6 = 10 mins

2) The Time that all the passengers are inside the tunnel = time taken by the train to cross the tunnel AFTER the moment the entire train is inside the tunnel.

So the distance that the train has to cover = 5000m - 500m = 4500m

So, time taken = 4500 / (30,000/60) = 9 mins

Hence the difference is 1 min. Ans A.

Bunuel, VeritasKarishma, please let us know the logic behind each of our approaches.
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 25 Apr 2019, 04:55
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mangamma
A train 500 metres long is crossing a tunnel 5 kilometres long at a speed of 30 kilometres per hour. What is the difference in the time in minutes for which all the passengers of the train are inside the tunnel and the time for which a particular passenger is inside the tunnel?

A. 1
B. 1.5
C. 2
D. 3
E. 5
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Time for which one passenger is inside the tunnel (say sitting right in front) = Time taken by the front of train to reach from the entry of tunnel to the exit of tunnel (a distance of 5000 m)
= 5 km/30 kmph = 10 mins

Time for which all passengers are inside the tunnel = Time at which the train's front is 500 m inside the tunnel to the time the front takes to reach the exit (a distance of 4500 m)
= 4.5/30 = 9 min

Time diff = 1 min

Alternatively,

The difference between the two times is the time it takes the front of the train to reach from the tunnel's entry to 500 m inside the tunnel
= .5 km / 30 kmph = 1 min
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 19 Apr 2019, 22:51
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The time that any one person is inside the tunnel is equal to the time taken by the train to travel the length of the tunnel which is (5/30)=1/6 hour=10 minutes.....(i)
The time that all the persons in the train are inside the tunnel is equal to the time taken by the train to travel the length of the tunnel plus the time it takes to travel it's own length which is equal to 10+(0.5*60/30)=11 minutes.
Difference:11-10=1. Ans: A
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 25 Apr 2019, 00:32
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Relative distance covered by train in reference to a person standing outside the train= 500m
speed of train= 30kmph or 50/6 m/s
Time taken= 500/(50/6)=60 sec or 1 min
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 25 Apr 2019, 00:47
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mangamma
A train 500 metres long is crossing a tunnel 5 kilometres long at a speed of 30 kilometres per hour. What is the difference in the time in minutes for which all the passengers of the train are inside the tunnel and the time for which a particular passenger is inside the tunnel?

A. 1
B. 1.5
C. 2
D. 3
E. 5
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Difference = length of train / speed of train = 0.5/30 hours = 1 minute.

Option (A).
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 30 Aug 2021, 06:42
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Converting 30 km/hr to m/s = 30*5/18 = 25/3 m/s

500/(25/3) = 60s = 1 min

A
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 20 Feb 2024, 03:18
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­I made the question this way:

|-----|-------------------------------------------------------|
0    500                                                           5000

0 is where the singular individual starts, and it ends at 5000m (5km).

500 is where the train starts because it is the time when the entire train is inside the tunnel, and consequently, all the people are in it.

Time passenger = \(\frac{5(distance)}{30(speed)}\)
Time entire train = \(\frac{5-0.5}{30}\)

Difference = \(\frac{5}{30} - \frac{4.5}{30} = \frac{0.5}{30} = 1min\)­­
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 23 Apr 2026, 20:03
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But during exit as well we must add 500m just the. way we added during entry
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A train 500 metres long is crossing a tunnel 5 kilometres long at a 23 Apr 2026, 21:43
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A train 500 metres long is crossing a tunnel 5 kilometres long at a speed of 30 kilometres per hour. What is the difference in the time in minutes for which all the passengers of the train are inside the tunnel and the time for which a particular passenger is inside the tunnel?

A. 1
B. 1.5
C. 2
D. 3
E. 5

A particular passenger is inside the tunnel for the time needed to cover 5 km:
5/30 hour = 10 minutes

All passengers are inside the tunnel only while the whole 500 m train fits completely inside the 5 km tunnel, so the relevant distance is:
5 - 0.5 = 4.5 km

Time = 4.5/30 hour = 9 minutes

Difference = 10 - 9 = 1 minute

Answer: A.

P.S. The wording is not perfect...

athakar7
But during exit as well we must add 500m just the. way we added during entry
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No. That extra 500 m is added when you want the train to completely clear the tunnel. Here, the question asks for the time during which all passengers are inside the tunnel, and that starts when the last passenger enters and ends when the first passenger starts to exit, so the interval is tunnel length - train length, not tunnel length + train length.
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