A train traveling at 72 kmph crosses a platform in 30 seconds and a ma

Question

A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

A. 240 meters
B. 360 meters
C. 420 meters
D. 600 meters
E. Cannot be determined

BrentGMATPrepNow · Accepted Answer

Let's use some graphics to help see what's happening here.

We'll say that the train STARTS crossing the platform when the front nose of the train meets the beginning edge of the platform . . . 
 https://i.imgur.com/qvFFu5M.png

. . . and the train FINISHES crossing the platform when the back end of the train cross the end of the platform . . . 
 https://i.imgur.com/hERlnNm.png

Let p = length of platform (in meters)
Let t = length of train (in meters)

We'll also add a  blue  dot at the front of train to help determine the distance the train travels.
Below, we have the train when it first meets the platform 
 https://i.imgur.com/DDzDVog.png

Below, we have the train when it FINISHES crossing the platform 
 https://i.imgur.com/8aBiryw.png

During this period, the total DISTANCE the train (and the  blue  dot) travels =  p + t meters

IMPORTANT: At this point, we better convert all units to meters and seconds.

GIVEN: A train traveling at 72 kmph crosses a platform in 30 seconds 
1 kilometer = 1000 meters
So, 72 kilometers per hour = 72000 meters per hour

There are 3600 seconds in an hour.
So, 72000 meters per hour = 72000 meters per 3600 seconds
= 20 meters per second     
So, the train's speed = 20 meters per second

Distance = (speed)(time) 
So, if the train travels for 30 seconds at a speed of 20 meters per second, the distance traveled = (20)(30) =  600  meters

We already know that the train travels =  p + t meters 
So, we can write:  p + t = 600

GIVEN: A train traveling at 72 kmph crosses a man standing on the platform in 18 seconds 
NOTE: I'd prefer that the question asked "Which of the following BEST APPROXIMATES is the length of the platform in meters?", since the width of the man will affect the calculations. 
So, let's just say the man does not have a width (width = 0)

So, here's the part where the train MEETS the man . . . 
 https://i.imgur.com/CX971XA.png

And here's the part where the train finishes PASSING the man . . . 
 https://i.imgur.com/NveGk90.png

In this case, the train travels a total distance of t meters.

Distance = (speed)(time) 
So, if the train travels for 18 seconds at a speed of 20 meters per second, the distance traveled = (20)(18) =   360   meters
We already know that the DISTANCE the train travels =   t   meters
So, we can write:   t = 360

At this point, we know that: 
 p + t = 600 
  t = 360

Subtract the bottom equation from the top equation to get: p = 240

Answer: A

Cheers,
Brent

Kurtosis · Answer

Speed of the train in metres/sec = 72000/3600 = 20

Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform

Distance travelled by train to cross the man = 18 * 20 = 360 = Length of train

Length of platform = 600 - 360 = 240

Answer: A

raarun · Answer

What if the the position man is standing is not a point but rather say .004 meters(may be a real fat one)
in that case it would
Distance travelled by train to cross the man = 18 * 20 = 360 = Distance occupied by man in platform + Length of train
The answer has to be E

Kurtosis · Answer

I do not think that we have to go into such minute detail and include the length of the person's waist as its negligible when compared to the overall length.

chetan2u · Answer

hi,
 Vyshak  is correct..
Don't complicate the Q, where it is not required..
If you want to have E as the answer, you don't require a fat person of .004m, even a thin guy of .001m will also effect the distance by that small amount..
But that is not required, we take the person as a point.

olischmied · Answer

Why do we have to subtract 18*20 from 30*20?

I don´t really get the connection between the two numbers. 
Maybe someone can explain how the fact that the train needs 18 seconds to pass the person is related to the length of the platform?

gracie · Answer

first find length of train:
18 s=1/200 h
72 kh*1/200 h=9/25 k=length of train
next find length of platform (p):
30 s=1/120 h
72 kh*1/120 h=9/25 k+p
p=6/25 k=240 m

DensetsuNo · Answer

Well\; this\; was\; fun.

We\; have\; to\; take\; into\; consideration\; the\; lenght\; of\; the\; train\; in\; this\; problem,\; 
 considering\; the\; time\; it\; takes\; the\; head\; of\; the\; train\; 
 to\; go\; from\; the\; start\; of\; the\; platform\; to\; the\; end\; of\; it.\;

\mbox{S}o\; if\; it\; takes\; take\; train\; 18\; seconds\; to\; pass\; a\; standing\; man,\; 
 it\; means\; that\; the\; lenght\; of\; the\; train\; was\; 72*\frac{1000}{3600}\; =\; 20\; *\; 18\; ->\; 360\; metres.

Found\; the\; lenght\; we\; simply\; need\; to\; do\; 20*30\; ->\; 600\; 
 which\; is\; the\; time\; the\; train\; takes\; to\; completely\; leave\; the\; platform\;

and\; subtract\; the\; lenght\; of\; the\; train:\; 600-360\; =\; 240

Answer\; A.

arhumsid · Answer

In speed-distance questions, always remember-
Pole, a man (stationary) etc are considered as points, when a train crosses these, it means that the train travelled a distance equal to its own length.
while,
Other trains, railway platform etc are considered for their own lengths, it means that if a moving train crosses these, the train travelled a distance equal to its own length + length of the other train/platform

Coming to this question:
Speed of the train: 72 km/h =  72*\frac{5}{18}  = 20 meters/sec ----(converting into mt/sec as everything else is in meters and seconds)

Train crosses a man (a stationary point) in 18 secs: Train covers its own length in 18 secs:
Length of train =  20 * 18 = 360  meters

Train crosses a platform in 30 secs: Train covers a distance equal to its own length+length of the platform in 30 secs:
i.e. length of the train + Length of the platform = 20 * 30 ----(Distance = Speed * Time)
 360+x = 600 
 x = 240

Length of the platform = 240 meters

A

JeffTargetTestPrep · Answer

We can let p = the length of the platform, in meters, and t = the length of the train, in meters.

When we say the train crosses a platform in 30 seconds, it really means it takes 30 seconds for the nose of the train to enter one end of the platform and the rear of the train to exit the other end of the platform. Thus, in 30 seconds, not only does the train’s nose travel the entire length of the platform but also its entire body length does. Thus, we have (notice that 72 kmph = 72000 meters per hour, and 30 sec = 30/3600 = 1/120 hr):

72000 x 1/120 = p + t

600 = p + t

p = 600 - t

We are also given that the train crosses a man (whose body width is negligible) standing on the platform in 18 seconds. So when the train crosses him, it only travels its body length in 18 seconds. Thus we have (notice that 18 sec = 18/3600 = 1/200 hr):

72000 x 1/200 = t

360 = t

Therefore, the platform has a length of 600 - 360 = 240 meters.

Answer: A

akadiyan · Answer

A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

A. 240 meters
B. 360 meters
C. 420 meters
D. 600 meters
E. Cannot be determined

Step 1:
To cross the platform = 72 km/h = 72 km/60 minutes = 1.2 km/60 seconds = 0.6 km/30 seconds = 600 meters

Step 2:
To cross the man = 72 km/h = 72 km/60 minutes = 1200 meter/60 seconds , 18 seconds =360 Meters

Step 3:
Length of platform = 600 - 360 = 240

Ans:   A

Mo2men · Answer

Hi Brent GMATPrepNow This explanation is elegant and magnificent. Thanks for you effort

BrentGMATPrepNow · Answer

Thanks for taking the time to say that!

Cheers,
Brent

Jawad001 · Answer

A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

A. 240 meters
B. 360 meters
C. 420 meters
D. 600 meters
E. Cannot be determined
Given that, the speed of train = 72 kmph = 72(5/18) msec
 = 20 msec
(The distance of train )/(Speed of train) = time 
x/20 = 18
X = 260
In case of crossing platform,
(The distance of train+The distance of Platform )/(Speed of train) = Time
(y+360)/20 = 30
Y + 360 = 600
Y = 240(A)

Fdambro294 · Answer

72 kmph = (72,000 meters) / (3,600 seconds) = 20 met/sec

To entirely cross the platform, the train has to cover its own length(L) plus the length of the platform (P)

In 30 seconds traveling at 20 met/sec ——— train can cover distance of ( L + P) meters

(20) (30) = L + P

To cross the man, all the train has to do is put its own length (L) in front of the man. Since the train does this in 18 seconds at the same speed

(20) (18) = L

Subtract the 2nd equation from the 1st equation

P = (30) (20) - (20) (18)

P = (20) (30 - 18)

P = 20 * 12 = 240 meters

A

Posted from my mobile device

TarunKumar1234 · Answer

Difference between time = 30-18 = 12 sec= Time required to pass distance equals to Platform As Speed = Distance /Time or, Distance = 72* \frac{12}{(60*60)} = 0.24 Km So, I think A.

Kinshook · Answer

Given: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds.
Asked: What is the length of the platform in meters?

72kmph = 72*1000/60*60 = 20 m/s

Length of the train = 20 * 18 = 360 m
Length of the train + Length of the platform = 20 * 30 = 600 m
Length of the platform = 600 - 360 = 240 m

IMO A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A train traveling at 72 kmph crosses a platform in 30 seconds and a ma

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A train traveling at 72 kmph crosses a platform in 30 seconds and a ma

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards