A train 500 metres long is crossing a tunnel 5 kilometres long at a

Question

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

GMATaspirant641 · Accepted Answer

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.

KarishmaB · Answer

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

effatara · Answer

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

nick1816 · Answer

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

GyanOne · Answer

Difference = length of train / speed of train = 0.5/30 hours = 1 minute.

Option (A).

rvgmat12 · Answer

Converting 30 km/hr to m/s = 30*5/18 = 25/3 m/s

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

A

Lodz697 · Answer

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

athakar7 · Answer

But during exit as well we must add 500m just the. way we added during entry

Bunuel · Answer

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. 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...

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 .

A train 500 metres long is crossing a tunnel 5 kilometres long at a

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A train 500 metres long is crossing a tunnel 5 kilometres long at a

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615 to 715 in 15 Days (Ria's Strategies)

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