• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code ## Trains from two opposite ends tagged by: Brent@GMATPrepNow This topic has 5 expert replies and 1 member reply oquiella Master | Next Rank: 500 Posts Joined 12 May 2015 Posted: 164 messages Upvotes: 3 #### Trains from two opposite ends 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 ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11204 messages Followed by: 1222 members Upvotes: 5254 GMAT Score: 770 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 Check out the online reviews of our course Come see all of our free resources 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! ### GMAT/MBA Expert Scott@TargetTestPrep GMAT Instructor Joined 25 Apr 2015 Posted: 691 messages Followed by: 3 members Upvotes: 43 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 ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2542 messages Followed by: 116 members Upvotes: 1153 GMAT Score: 770 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

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

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13760 messages
Followed by:
1802 members
13060
GMAT Score:
790
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.

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

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9086 messages
Followed by:
472 members
2867
GMAT Score:
800
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'...

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

_________________
Contact Rich at Rich.C@empowergmat.com

sandipgumtya Master | Next Rank: 500 Posts
Joined
07 Jun 2014
Posted:
126 messages
3
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.

### Best Conversation Starters

1 Roland2rule 181 topics
2 lheiannie07 110 topics
3 ardz24 60 topics
4 LUANDATO 55 topics
5 swerve 52 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

153 posts
2 GMATGuruNY

The Princeton Review Teacher

125 posts
3 Scott@TargetTestPrep

Target Test Prep

123 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 EconomistGMATTutor

The Economist GMAT Tutor

83 posts
See More Top Beat The GMAT Experts