by: Dexter43
27 mins
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
54% (03:04) correct
46%
(03:11)
wrong
based on 168
sessions
History
Date
Time
Result
Not Attempted Yet
How much time will an express train of length 150 meters and running at a speed of 75 kmph take to cross a man walking at 5 m/s inside a passenger train of length 200 meters and running at 15 kmph in a direction opposite to that of the express train. The man is walking inside the train and in opposite direction to that of the train. (Assume the man does not reach the end of his train meanwhile.)
A. 5 sec
B. 6 sec
C. 7.5 sec
D. 8 sec
E. 10 sec
_________________
A. 5 sec
B. 6 sec
C. 7.5 sec
D. 8 sec
E. 10 sec
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
ishant5243
It's a very simple question if you ignore the length of the passenger train altogether. Just assume that there is an express train running at 75 km/hr and you need to calculate the time it needs to overtake a person walking/running in the same direction on road at speed of 3km/hr( speed of the person in train(18km/hr) - speed of passenger train in opposite direction(15km/hr)).
So now all you need is to divide the length of the express train(150 m) with the relative speed of the express train and person - 72km/hr.
(150*60*60)/72*1000 = 7.5 sec
Please help with Kudos if it helps.
It's a very simple question if you ignore the length of the passenger train altogether. Just assume that there is an express train running at 75 km/hr and you need to calculate the time it needs to overtake a person walking/running in the same direction on road at speed of 3km/hr( speed of the person in train(18km/hr) - speed of passenger train in opposite direction(15km/hr)).
So now all you need is to divide the length of the express train(150 m) with the relative speed of the express train and person - 72km/hr.
(150*60*60)/72*1000 = 7.5 sec
Please help with Kudos if it helps.
General Discussion
TestPrepUnlimited
Expert
Tutor
Joined: 16 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,221
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert reply
Bunuel
The speed of the express train is the opposite of that of the passenger train and the man walking inside the passenger train.
Therefore the other two speeds are working against the express train.
We can add all the speeds together and treat the entire system as one object. Hence treating the man and passenger train as stationary, the express train has a speed of:
75 km/h + 15 km/h + 5 m/s = 90 km/h + 5 m/s = 90 * 5/18 m/s + 5 m/s = 30 m/s.
The total distance we need to travel however is only 150 meters since the express train is only 150 meters long (or think of it as the time needed for the man to pass the 150-meter express train). Therefore 150 m / (30 m/s) = 5s is the answer.
Ans: A
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. !
TestPrepUnlimited
So according to the question the man is walking from the front of the passenger train to the back so
75 km/h + 15 km/h - 5 m/s = 90 km/h + 5 m/s = 90 * 5/18 m/s - 5 m/s = 20 m/s.
that means that 150/20=7.5 and answer C
also 5M/sec isn't exactly walking
ishant5243
Joined: 13 May 2018
Last visit: 27 May 2022
Posts: 12
Location: India
Schools: Ross '24 (II)
GMAT 1: 700 Q50 V35
GRE 1: Q170 V155
GPA: 3.36
@Bunuel; can you please help with the solution to this problem.
kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
Posts: 580
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
GPA: 4
Products:
It would be helpful to first analyze the man from the ground frame of reference.
The man is inside a train that is moving towards left with a speed of 15kmph or 25/6 mps and the man himself is moving towards right with a speed of 5 mps.
Therefore, from a ground reference, the man is actually moving rightwards with a speed of 5 - 25/6 = 5/6 mps
Now we bring in the express train which is moving rightwards with a speed of 75 kmph or 125/6 mps.
In the frame of reference of this express train, the man is stationary and the train is moving in rightwards direction with a speed of 125/6 - 5/6 = 20 mps
In order to cross the man, the train must cover a distance equivalent to its own length. This with a speed of 20 mps and a length of 150m, the train would take 150/20 = 7.5s to cross the man.
Hence, option C.
Posted from my mobile device
The man is inside a train that is moving towards left with a speed of 15kmph or 25/6 mps and the man himself is moving towards right with a speed of 5 mps.
Therefore, from a ground reference, the man is actually moving rightwards with a speed of 5 - 25/6 = 5/6 mps
Now we bring in the express train which is moving rightwards with a speed of 75 kmph or 125/6 mps.
In the frame of reference of this express train, the man is stationary and the train is moving in rightwards direction with a speed of 125/6 - 5/6 = 20 mps
In order to cross the man, the train must cover a distance equivalent to its own length. This with a speed of 20 mps and a length of 150m, the train would take 150/20 = 7.5s to cross the man.
Hence, option C.
Posted from my mobile device
similar question: https://gmatclub.com/forum/a-train-trav ... 15070.html though this time man is not stationary.
first calculate the net speed of man relative to passenger train:
passenger train: 15km/h = 25/6 m/s
man: opposite direction to passenger train at 5 m/s
their relative speed: 5-25/6 = 5/6 m/s in direction of man's movement.
express train: 75km/h = 125/6 m/s moves same direction to man.
speed of express train relative to man: 125/6 - 5/6 = 20 m/s
to cross the man, express train has to travel it's length of 150m (assuming man's width is negligible) hence the gap distance is of 150m
time it will take for that: 150/20 = 7.5 seconds
first calculate the net speed of man relative to passenger train:
passenger train: 15km/h = 25/6 m/s
man: opposite direction to passenger train at 5 m/s
their relative speed: 5-25/6 = 5/6 m/s in direction of man's movement.
express train: 75km/h = 125/6 m/s moves same direction to man.
speed of express train relative to man: 125/6 - 5/6 = 20 m/s
to cross the man, express train has to travel it's length of 150m (assuming man's width is negligible) hence the gap distance is of 150m
time it will take for that: 150/20 = 7.5 seconds
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.