Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Oct 2014, 04:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

At 1:00 PM, Train X departed from Station A on the road to

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jun 2010
Posts: 141
Concentration: Strategy, Technology
Followers: 6

Kudos [?]: 19 [1] , given: 26

Reviews Badge
At 1:00 PM, Train X departed from Station A on the road to [#permalink] New post 04 Oct 2010, 15:14
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

44% (02:40) correct 56% (02:21) wrong based on 128 sessions
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?

A. 0.5 + (p - 0.5s)/(r + s)
B. (p - 0.5s)/(r + s)
C. 0.5 + (p - 0.5r)/r
D. (p - 0.5r)/(r + s)
E. 0.5 + (p - 0.5r)/(r + s)
[Reveal] Spoiler: OA
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [5] , given: 2734

Re: Rates Question [#permalink] New post 04 Oct 2010, 15:41
5
This post received
KUDOS
Expert's post
krazo wrote:
Here is a tough rate question that took me some time to figure out the algebra for... give it a shot!
Quote:
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?


Quote:
    A. 0.5 + (p - 0.5s)/(r + s)
    B. (p - 0.5s)/(r + s)
    C. 0.5 + (p - 0.5r)/r
    D. (p - 0.5r)/(r + s)
    E. 0.5 + (p - 0.5r)/(r + s)


Rate of X - r miles per hour;
Rate of Y - s miles per hour;
Combined rate s+r miles per hour;
Distance between the stations p miles;

In 1/2 hours that X traveled alone it covered \frac{1}{2}*r miles, so together trains should cover p-\frac{1}{2}r=\frac{2p-r}{2} miles, which they will cover in \frac{\frac{2p-r}{2}}{r+s}=\frac{2p-r}{2(r+s)} hours.

Total time after 1:00 PM till they meet would be \frac{1}{2}+\frac{2p-r}{2(r+s)}=\frac{1}{2}+\frac{p-0.5r}{r+s} hours.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 22 Aug 2008
Posts: 186
Followers: 5

Kudos [?]: 56 [0], given: 11

Re: Rates Question [#permalink] New post 04 Oct 2010, 16:30
The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s

From 1:30, time is going to take when they meet = (p-.5r)/(r+s)

so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]

ans is E
Intern
Intern
avatar
Joined: 30 Jul 2013
Posts: 7
Concentration: Organizational Behavior, General Management
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 1 [0], given: 3

GMAT ToolKit User CAT Tests
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink] New post 16 Sep 2014, 19:23
Hello Bunnel,

This definitely is a good procedure to solve this problem. But, may I know if this can be solved using picking up numbers or any easier method? IF yes, could you please share.

Pretz
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4815
Location: Pune, India
Followers: 1134

Kudos [?]: 5195 [0], given: 164

Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink] New post 16 Sep 2014, 22:16
Expert's post
krazo wrote:
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?

A. 0.5 + (p - 0.5s)/(r + s)
B. (p - 0.5s)/(r + s)
C. 0.5 + (p - 0.5r)/r
D. (p - 0.5r)/(r + s)
E. 0.5 + (p - 0.5r)/(r + s)



You can do it by plugging in numbers though with so many variables, it is hard to keep track of values for each.

Preferable here would be algebra (use relative speed concepts):

Time taken to meet starting from 1:30 = \frac{Total Distance}{Total Speed} = \frac{p - r/2}{r + s}
Note that since X covers first half hour alone, it covers r*0.5 distance alone so distance between the two trains at 1:30 is (p - r/2).

But we need the time taken from 1 onwards so time taken = 0.5 + \frac{p - r/2}{r + s}

Here is a post that discusses relative speed (including a similar trains example): http://www.veritasprep.com/blog/2012/07 ... elatively/

Solving using Plugging in:

Say p = 100, r = 100, s = 50.
X runs for half an hour and covers 50 miles in that time. So now X and Y are 50 miles apart.
Total time taken to cover 50 miles = 50/(100+50) = 1/3 hr
Total time taken to cover 100 miles = 1/2 + 1/3 = 5/6

Now put these values in the options. Remember, there are symmetrical options in r and s so you need to take different values for r and s.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: At 1:00 PM, Train X departed from Station A on the road to   [#permalink] 16 Sep 2014, 22:16
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Train X departs Rockburg for Williamsland at 1:00 p.m. and madimo 7 10 Oct 2012, 03:04
A train traveled from station X to station Y at a constant seofah 2 09 Nov 2008, 07:10
A train traveled from station X to station Y at a constant singh_amit19 4 24 Sep 2007, 12:15
Train A leaves the station at 5PM and travels North at the leeye84 5 13 Jul 2007, 11:19
Time Amount 1:00 P.M. 10.0 grams 4:00 P.M. x grams 7:00 P.M. gmatornot 9 22 Aug 2006, 21:29
Display posts from previous: Sort by

At 1:00 PM, Train X departed from Station A on the road to

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.