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

 It is currently 10 Feb 2016, 10:28

### 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

Author Message
TAGS:
Manager
Joined: 24 Jun 2010
Posts: 141
Concentration: Strategy, Technology
Followers: 6

Kudos [?]: 24 [1] , given: 26

At 1:00 PM, Train X departed from Station A on the road to [#permalink]  04 Oct 2010, 15:14
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

46% (02:44) correct 54% (02:23) wrong based on 209 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
Math Expert
Joined: 02 Sep 2009
Posts: 31295
Followers: 5356

Kudos [?]: 62330 [4] , given: 9454

Re: Rates Question [#permalink]  04 Oct 2010, 15:41
4
KUDOS
Expert's post
2
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.

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

Kudos [?]: 75 [0], given: 11

Re: Rates Question [#permalink]  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
Joined: 30 Jul 2013
Posts: 25
Concentration: Technology, General Management
GMAT Date: 07-03-2015
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 11 [1] , given: 25

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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6229
Location: Pune, India
Followers: 1678

Kudos [?]: 9620 [0], given: 197

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

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

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 8208
Followers: 417

Kudos [?]: 111 [0], given: 0

Re: At 1:00 PM, Train X departed from Station A on the road to [#permalink]  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.
_________________
Re: At 1:00 PM, Train X departed from Station A on the road to   [#permalink] 18 Dec 2015, 07:03
Similar topics Replies Last post
Similar
Topics:
3 At 1:00, Jack starts to bicycle along a 60 mile road at a constant spe 6 13 Feb 2015, 07:40
15 Train A left station T at 3:30 p.m. and traveled on straight 4 28 Dec 2013, 04:29
8 Trains A and B start simultaneously from stations 300 miles 9 16 Apr 2013, 05:58
4 A train travels from station A to station B. If it travels 6 16 Sep 2012, 01:48
12 A train met with an accident 60km away from station A. It co 12 18 Oct 2011, 06:37
Display posts from previous: Sort by