GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2018, 20:19

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# Train X leaves New York at 1 A.M. and travels east at a speed of x mil

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51035
Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

30 Oct 2017, 23:03
00:00

Difficulty:

15% (low)

Question Stats:

86% (02:10) correct 14% (02:34) wrong based on 180 sessions

### HideShow timer Statistics

Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

(A) 5x/6
(B) 9x/8
(C) 6x/5
(D) 9x/7
(E) 3x/2

_________________
##### Most Helpful Expert Reply
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4261
Location: United States (CA)
Re: Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

01 Nov 2017, 16:07
2
3
Bunuel wrote:
Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

(A) 5x/6
(B) 9x/8
(C) 6x/5
(D) 9x/7
(E) 3x/2

Since we have a catch-up problem, we can use the formula: Distance 1 = Distance 2.

The rate of train X is x, and the time is 4.5 hours. We can let the rate of train Z = r, and the time is 3.5 hours. Thus:

4.5x = 3.5r

45x = 35r

9x = 7r

9x/7 = r

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

##### General Discussion
Intern
Joined: 09 Oct 2017
Posts: 2
Re: Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

31 Oct 2017, 00:28
I would go for (D).

Train X travels with a speed of x=d/4.5 (1.00am to 5.30am), Train Z travels with a speed of v=d/3.5 (2.00am to 5.30am).

Now if d=4.5 {miles}, Train X travels with a speed of x=1. Train Z travels with a speed of v=4.5/3.5=9/7.

So, for x=1, 9x/7=9/7, hence option (D).
Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

03 Nov 2017, 07:37
Bunuel wrote:
Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

(A) 5x/6
(B) 9x/8
(C) 6x/5
(D) 9x/7
(E) 3x/2

This question can be approached with the "close the gap in a chase" method, and by choosing numbers.

Train A, when traveling alone, creates the distance between A and B. That's the gap.

When Train B starts moving, the chase is on.
Time = 3.5 hours
B chases A, closes the gap, only while both move.

B closes the gap at a relative speed, r, of (B's rate - A's rate). What is r? rt = D, so...

The gap will close at D/t = r.

To find r, pick an easy "gap" distance: 70 mi (because t = 3.5)

A travels for 1hr, A's rate = 70 mph = x

The distance/gap of 70 mi is closed by relative speed of (B-A)

Relative speed? D/t = r
70/3.5 = 20
The difference between A's speed and B's speed is 20 mph.

B is chasing; B travels at 20 mph faster than A

B's speed: (70 + 20) = 90 mph

With x = 70, check choices until the answer is 90.

(A) 5x/6 = 350/6 = 5_. No

(B) 9x/8 = 6300/8 = 7_. No

(C) 6x/5 = 4200/5 = 8_. No

(D) 9x/7 = 6300/7= 90. MATCH

(E) 3x/2 = 210/2 = 105. No

Answer D
Manager
Joined: 03 May 2014
Posts: 160
Location: India
WE: Sales (Mutual Funds and Brokerage)
Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

04 Nov 2017, 20:54
let the speed of train X=10m/hr
It has traveled from 1 am till 5.30am, total of 4.5 hrs
Distance=10*4.5=45 miles
This distance has to be covered by train z in 3.5 hrs(it travels from 2 am to 5.30am)
let the speed of z=s
45=sx3.5=450/35=90/7
Now in answer choice plugin value of speed of train X=10
the correct answer is D=90/7
CEO
Joined: 11 Sep 2015
Posts: 3222
Location: Canada
Re: Train X leaves New York at 1 A.M. and travels east at a speed of x mil  [#permalink]

### Show Tags

08 Jun 2018, 05:44
Top Contributor
Bunuel wrote:
Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

(A) 5x/6
(B) 9x/8
(C) 6x/5
(D) 9x/7
(E) 3x/2

Train X leaves at 1 A.M. and Train Z leaves New York at 2 A.M.
When they meet at 5:30 A.M., Train X's travel time will be 4.5 hours, and Train Z's travel time will be 3.5 hours
Also recognize that, when the trains meet, they both will have traveled the same distance.

We know that Train X travels at x mph, and we want to find Train Z's speed.
So, let z = Train Z's speed (in mph)

Now let's create an equation we can work with!

Let's start with a word equation:
Distance traveled by Train X = Distance traveled by Train Z
distance = (time)(speed)

So, we get: (4.5 hours)(x mph) = (3.5 hours)(y mph)
Simplify: 4.5x = 3.5y
Solve for y to get: = 4.5x/3.5
Check answer choices....not there.
So, take 4.5x/3.5, and multiply top and bottom by 2 to get the EQUIVALENT fraction: 9x/7
Check answer choices....answer: D

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

Re: Train X leaves New York at 1 A.M. and travels east at a speed of x mil &nbs [#permalink] 08 Jun 2018, 05:44
Display posts from previous: Sort by

# Train X leaves New York at 1 A.M. and travels east at a speed of x mil

 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®.