It is currently 18 Jan 2018, 07:56

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

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

### Hide Tags

Manager
Joined: 24 Jun 2010
Posts: 140

Kudos [?]: 45 [1], given: 26

Concentration: Strategy, Technology
At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

04 Oct 2010, 15:14
1
KUDOS
16
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

46% (01:48) correct 54% (02:20) wrong based on 305 sessions

### HideShow timer Statistics

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

Kudos [?]: 45 [1], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139397 [4], given: 12789

Re: Rates Question [#permalink]

### Show Tags

04 Oct 2010, 15:41
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 139397 [4], given: 12789

Manager
Joined: 22 Aug 2008
Posts: 181

Kudos [?]: 105 [0], given: 11

Re: Rates Question [#permalink]

### Show Tags

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

Kudos [?]: 105 [0], given: 11

Intern
Joined: 30 Jul 2013
Posts: 47

Kudos [?]: 17 [1], given: 27

Concentration: Technology, General Management
GMAT Date: 07-03-2015
GPA: 3.8
WE: Information Technology (Computer Software)
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

16 Sep 2014, 19:23
1
KUDOS
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
_________________

On the Kudos Spree.

If you like my post/comment please appreciate with kudos

Kudos [?]: 17 [1], given: 27

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7866

Kudos [?]: 18468 [0], given: 237

Location: Pune, India
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

16 Sep 2014, 22:16
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

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18468 [0], given: 237

Non-Human User
Joined: 09 Sep 2013
Posts: 14243

Kudos [?]: 291 [0], given: 0

Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

18 Dec 2015, 07:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 14243

Kudos [?]: 291 [0], given: 0

Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

22 Mar 2017, 00:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2028

Kudos [?]: 1084 [1], given: 4

Location: United States (CA)
At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

23 Mar 2017, 15:57
1
KUDOS
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)

We have a converging rate problem in which we can use the following formula:

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

Train X is traveling at a rate of r mph and train Y is traveling at a rate of s mph. Since train X left at 1:00 PM and train Y left at 1:30 PM, we can let the time of train Y = t and the time of train X = t + 0.5.
Thus:

r(t + 0.5) + st = p

rt + 0.5r + st = p

t(r + s) = p - 0.5r

t = (p - 0.5r)/(r + s)

However, t is relative to train Y, which left at 1:30 PM. Since we want the time relative to 1:00 PM, we need to add 0.5 hour to t; thus, the time needed for the two trains to pass each other is 0.5 + (p - 0.5r)/(r + s).

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1084 [1], given: 4

Manager
Joined: 01 Jun 2015
Posts: 200

Kudos [?]: 58 [0], given: 114

Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

25 Mar 2017, 06:49
ScottTargetTestPrep wrote:
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)

We have a converging rate problem in which we can use the following formula:

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

Train X is traveling at a rate of r mph and train Y is traveling at a rate of s mph. Since train X left at 1:00 PM and train Y left at 1:30 PM, we can let the time of train Y = t and the time of train X = t + 0.5.
Thus:

r(t + 0.5) + st = p

rt + 0.5r + st = p

t(r + s) = p - 0.5r

t = (p - 0.5r)/(r + s)

However, t is relative to train Y, which left at 1:30 PM. Since we want the time relative to 1:00 PM, we need to add 0.5 hour to t; thus, the time needed for the two trains to pass each other is 0.5 + (p - 0.5r)/(r + s).

ScottTargetTestPrep

Sir,

I approached on your method.But I solved the equation in the following way:

p=rt+s(t-0.5)---->I subtracted 1/2 hour from the time taken by the train Y. Is that wrong??

Kudos [?]: 58 [0], given: 114

Intern
Joined: 06 Jul 2014
Posts: 5

Kudos [?]: 5 [5], given: 12

Location: India
GPA: 3.5
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

25 Mar 2017, 08:26
5
KUDOS
the total distance between the stations be P

SPeed of X is r

SPeed of Y is S

when the trains are moving in the opposite direction then we add the speeds

Therefore total time taken should be p/r+s.

But Train X has already covered distance equal to 0.5r

hence the answer is option E

Kudos [?]: 5 [5], given: 12

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2028

Kudos [?]: 1084 [0], given: 4

Location: United States (CA)
Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]

### Show Tags

29 Mar 2017, 09:00
Expert's post
1
This post was
BOOKMARKED
techiesam wrote:
ScottTargetTestPrep wrote:
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)

We have a converging rate problem in which we can use the following formula:

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

Train X is traveling at a rate of r mph and train Y is traveling at a rate of s mph. Since train X left at 1:00 PM and train Y left at 1:30 PM, we can let the time of train Y = t and the time of train X = t + 0.5.
Thus:

r(t + 0.5) + st = p

rt + 0.5r + st = p

t(r + s) = p - 0.5r

t = (p - 0.5r)/(r + s)

However, t is relative to train Y, which left at 1:30 PM. Since we want the time relative to 1:00 PM, we need to add 0.5 hour to t; thus, the time needed for the two trains to pass each other is 0.5 + (p - 0.5r)/(r + s).

ScottTargetTestPrep

Sir,

I approached on your method.But I solved the equation in the following way:

p=rt+s(t-0.5)---->I subtracted 1/2 hour from the time taken by the train Y. Is that wrong??

Mathematically, you can solve it the way you did. You let t represent the time counting from 1 p.m., and thus t - ½ was the time counting from 1:30 p.m.

However, after you solve for t, in terms of p, r, and s, you see that the equivalent expression of t is not in any of the answer choices. That is why in my solution, I made t relative to 1:30 p.m. rather than 1 p.m.
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1084 [0], given: 4

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 306 [0], given: 17

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

### Show Tags

29 Mar 2017, 18:24
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)

distance X travels alone in 0.5 hours=.5r miles
time X and Y travel together from 1:30 to passing=(p-.5r)/(r+s) hours
total time from 1PM to passing=0.5+(p-.5r)/(r+s) hours
E

Kudos [?]: 306 [0], given: 17

At 1:00 PM, Train X departed from Station A on the road to   [#permalink] 29 Mar 2017, 18:24
Display posts from previous: Sort by

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

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

 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®.