It is currently 24 Feb 2018, 04:06

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Train X and train Y pass one another traveling in opposite directions.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43894
Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 04:56
2
This post received
KUDOS
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:52) correct 25% (02:17) wrong based on 327 sessions

HideShow timer Statistics

Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80


Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Intern
Intern
avatar
Joined: 17 Feb 2015
Posts: 28
GPA: 3
Reviews Badge
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 05:45
1
This post received
KUDOS
Let's say train X runs at z miles/hour, then train Y will be running at (z-30) miles/hour
Since they are 100 miles apart after 40 minutes = 40/60 hours = 2/3 hours

\(z*\frac{2}{3} + (z-30)*\frac{2}{3} = 100\)
\(2*z*\frac{2}{3} -20 = 100\)
\(z*\frac{2}{3} = 60\) = distance travelled by train X in 40 minutes.
7 KUDOS received
Intern
Intern
avatar
Joined: 13 Jan 2015
Posts: 14
GMAT 1: 750 Q50 V41
GPA: 3.86
Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 07:02
7
This post received
KUDOS
1
This post was
BOOKMARKED
The easiest way to think about this problem is to start off conceptually.

If the total distance between the trains after 2/3 hours (40 minutes) is 100 miles, then the combined speed of the trains must be 150 mph. (using RTD tables, 100 * 3/2 = 150)
Therefore, if train x is going 30 mph faster than train y, then train x's speed must be -> x + (x-30) = 150 -> x = 90

Therefore, after 40 minutes, traveling at 90 mph, train x has traveled 60 miles (90 * 2/3 hours = 60 miles).

Last edited by robertsonsd on 26 Feb 2016, 20:51, edited 1 time in total.
2 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 578
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 08:50
2
This post received
KUDOS
Bunuel wrote:
Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80


Kudos for a correct solution.


x=Speed of Train X
y= X-30
relative speed = 2X-30
T= 2/3 hr

(2X-30) *2/3= 100
X=90 mph

distance travelled = 90*2/3 = 60

Answer C
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

2 KUDOS received
Manager
Manager
avatar
B
Joined: 24 Jan 2015
Posts: 67
GMAT 1: 590 Q39 V31
GPA: 4
WE: Consulting (Pharmaceuticals and Biotech)
Premium Member Reviews Badge CAT Tests
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 09:37
2
This post received
KUDOS
Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30

d=100 and t = 40 min i.e 40/60 hr

using RTD table, (2R+30) * 40/60 = 100 ==> R= 60 miles/hr

So the rate of train X is 90 miles/hr (since R+30)

The distance traveled by Train X in 40 min is R*T = 90 * 40?/60 = 60 miles (C)
1 KUDOS received
Current Student
User avatar
Status: Birds fly because they have wings, not because they have sky.
Joined: 21 Sep 2014
Posts: 216
Location: Singapore
Concentration: Strategy, Technology
GMAT 1: 740 Q50 V40
GPA: 3.65
WE: Information Technology (Consulting)
Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 27 Mar 2015, 20:06
1
This post received
KUDOS
Its a relative speed problem.

Relative speed of train X with reference to train Y = 100*60/40 = 150

Since train X and Y are going in opposite direction, the relative speed would be sum of individual speeds.
Hence,

x -30 + x = 150 => x=90.

Speed of train X is 90 and hence distance traveled in 40 minutes would be 90*40/60 = 60 miles.

C is the correct answer.
_________________

Regards,
J

--------------------------------------------------
Consider Kudos if I helped in some way!!!

Perseverance is the hard work you do after you get tired of doing the hard work you already did.

2 KUDOS received
Intern
Intern
avatar
Joined: 04 Mar 2015
Posts: 4
Premium Member
Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 28 Mar 2015, 22:56
2
This post received
KUDOS
Answer is "C"

if they travel 100 miles in 40 mins
=> in 1 hr they will travel (100/40)*60 = 150 miles
assume speed of train X = y+30
and seepd of 2nd train = y
now since the trains are moving in different directions the speed of both the trains add up
=> y + 30 + y = 150 (because in one 1 hr they travel 150 miles)
=> 2y + 30 = 150
=> y = 60
=> speed of train x = 90
hence in 40 mins it will travel 60 miles ( 90 *40/60)
Manager
Manager
avatar
S
Joined: 06 Jun 2013
Posts: 191
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE: Engineering (Computer Software)
Premium Member
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 21 Jun 2015, 06:59
let's say speed of y be a km/h and speed of x is (a+30)km/h
since they are traveling in opposite directions, we need to add their speed,
therefore total speed is a+a+30 =(2a+30)km/h
in 2/3 = 0.66 hours they traveled 100 km, so distance/time = speed
100/0.66=2a+30
a=60km/h
so speed of x is 60+30 = 90km/h
and x will cover 90*(2/3) = 60km
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 601
Schools: Cambridge'16
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 11 Oct 2015, 06:46
(2/3)x + (2/3)*(x+30)=100

(4/3)*x=80

x=60

60+30=90*(2/3)=60

C
CR Forum Moderator
User avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 529
GMAT ToolKit User
Re: Train X and train Y pass one another traveling in opposite directions. [#permalink]

Show Tags

New post 03 Feb 2018, 00:14
For relative speed of bodies moving in opposite direction, the equation is (Sx + Sy) X t = Distance

Here, total distance need to be covered is 100 miles

Let the speed of train Y is y. Therefore, the speed of train X would be y+30.

So, the equation becomes \((y+3+y)t=100=>y=60\)

So, the speed of train X is 60+30=90

In 60 minutes train x travels 90 miles. So in 40 minutes it will travel 60 miles.
_________________

Hasan Mahmud

Re: Train X and train Y pass one another traveling in opposite directions.   [#permalink] 03 Feb 2018, 00:14
Display posts from previous: Sort by

Train X and train Y pass one another traveling in opposite directions.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.