• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Trains from two opposite ends

This topic has 5 expert replies and 1 member reply
oquiella Master | Next Rank: 500 Posts Default Avatar
Joined
12 May 2015
Posted:
164 messages
Upvotes:
3

Trains from two opposite ends

Post Sun Sep 27, 2015 6:49 pm
Two trains X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had train X traveled when it met train Y.

A. 37.5
B. 40
C. 60
D. 62.5
E. 77.5

  • +1 Upvote Post
  • Quote
  • Flag
sandipgumtya Master | Next Rank: 500 Posts Default Avatar
Joined
07 Jun 2014
Posted:
126 messages
Upvotes:
3
Post Sun Sep 27, 2015 9:27 pm
Speed of Train X 20kmph and Train Y 100/3 kmph.Suppose they meet after T hrs time.So,20T+100/3 T=100.We ger T=15/8 .
So,Train X would travel 20*15/8=37.5 km before meeting Train Y.Ans- A IMO.
Experts can help explain better.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sun Sep 27, 2015 10:27 pm
Hi oquiella,

The answer choices to this question are 'spread out' enough that we can avoid much of the long-winded 'math' and do a couple of calculations (with a little estimation) to get to the solution.

Since we know how long each train takes to travel 100 miles, we can calculate their two speeds:

Train X: 100 miles in 5 hours = 20 miles/hour
Train Y: 100 miles in 3 hours = 33 1/3 miles/hour

Since these trains are approaching one another, they travel a TOTAL of 20 + 33 1/3 = 53 1/3 miles per hour.

The route is 100 miles, so it would take a little less than 2 hours for these two trains to travel that distance (and 'meet up'). We're asked how far Train X would have traveled at that point. Since the travel time is a little less than 2 hours and Train X travels at 20 miles/hour, Train X would have traveled LESS than 40 miles. There's only one answer that 'fits'...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Sep 28, 2015 3:01 am
oquiella wrote:
Two trains X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had train X traveled when it met train Y.

A. 37.5
B. 40
C. 60
D. 62.5
E. 77.5
Time and rate are RECIPROCALS.
Since the TIME RATIO for X and Y is (5 hours) : (3 hours), the RATE RATIO for X to Y is (3mph) : (5mph).
Implication:
When X and Y work together to travel the 100 miles between them, X travels 3 miles for every 5 miles that Y travels.
Thus, X will travel 3/8 of the 100-mile distance:
(3/8)(100) = 37.2.

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

DavidG@VeritasPrep Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
120 members
Upvotes:
1153
GMAT Score:
770
Post Mon Sep 28, 2015 5:17 am
Quote:
Two trains X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had train X traveled when it met train Y.

A. 37.5
B. 40
C. 60
D. 62.5
E. 77.5
Rate for X: 100/5 = 20 mph; Rate for Y: 100/3 = 33 1/3 mph.

Now use a bit of logic.

If the trains had been traveling at the same speed, then they'd each have covered 50 miles by the time they met. Because X is slower, X must have covered less than 50 miles. Eliminate C, D, and E.

Now test one of the two remaining answer choices. Let's try B, as it's a nice round number. If X has covered 40 miles, then it traveled for 2 hours at 20mph. But if Y traveled for 2 hours, it would have covered (33 1/3) * 2 = 66 2/3 miles. Together, the trains would have covered 40 + 66 2/3 mies, which is pretty clearly more than the 100 miles that separated them. That leaves us with A.

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post Thu Dec 07, 2017 9:25 am
oquiella wrote:
Two trains X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had train X traveled when it met train Y.

A. 37.5
B. 40
C. 60
D. 62.5
E. 77.5
Another approach:

Train X completed the 100-mile trip in 5 hours
Speed = distance/time
= 100/5
= 20 mph

Train Y completed the 100-mile trip in 3 hours
Speed = distance/time
= 100/3
33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y?
Let's start with a word equation.

When the two trains meet, each train will have been traveling for the same amount of time
So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed
We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels
So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation.
We get: d/20 = (100 - d)/33
Cross multiply to get: (33)(d) = (20)(100 - d)
Expand: 33d = 2000 - 20d
Add 20d to both sides: 53d = 2000
So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40
Since the denominator is greater than 50, we can conclude that 2000/53 is LESS THAN 40
Since only one answer choice is less than 40, the correct answer must be A

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post Tue Dec 12, 2017 7:15 am
oquiella wrote:
Two trains X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had train X traveled when it met train Y.

A. 37.5
B. 40
C. 60
D. 62.5
E. 77.5
We are given that train X completed the the 100-mile trip in 5 hours, and that train Y completed the 100-mile trip in 3 hours.

Since rate = distance/time, the rate of train X is 100/5 = 20 mph and the rate of train Y is 100/3 mph.

Since the trains left at the same time, we can let the time of each train = t.

We need to determine the distance traveled by train X when it met train Y. Since the two trains are “converging” we can use the formula:

distance of train X + distance of train Y = total distance

20t + (100/3)t = 100

Multiplying the entire equation by 3, we have:

60t + 100t = 300

160t = 300

t = 300/160 = 30/16 = 15/8.

Thus, train X and Y met each other after 15/8 hours.

Since distance = rate x time, the distance traveled by train X when it met train Y was:

15/8 x 20 = 300/8 = 75/2 = 37.5 miles.

Answer: A

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 67 first replies
2 Rich.C@EMPOWERgma... 44 first replies
3 Brent@GMATPrepNow 40 first replies
4 Jay@ManhattanReview 25 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

132 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

112 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

95 posts
4 image description Scott@TargetTestPrep

Target Test Prep

92 posts
5 image description Max@Math Revolution

Math Revolution

91 posts
See More Top Beat The GMAT Experts