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

 It is currently 21 Nov 2019, 21:57

### 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

# Trains A and B start simultaneously from stations 300 miles

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Sep 2012
Posts: 182
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

Updated on: 16 Apr 2013, 06:59
6
11
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:58) correct 20% (02:02) wrong based on 385 sessions

### HideShow timer Statistics

Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

Originally posted by skamal7 on 16 Apr 2013, 06:58.
Last edited by Bunuel on 16 Apr 2013, 06:59, edited 1 time in total.
Edited the question.
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1013
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

16 Apr 2013, 06:59
3
2
To solve problems involving trains that travel in opposite directions the first thing to do is sum their speeds.
50+40=90 m/h They will cover 300 miles (they will meet) after $$\frac{300}{90}$$ hours (space=time*speed , 300=t*90)
$$\frac{300}{90}=\frac{30}{9}=\frac{27}{9}+\frac{3}{9}=3 \frac{1}{3} h$$ They'll meet after 3 1/3 hours.
How many miles will A travel is 3 1/3 hours? $$50*\frac{10}{3} = \frac{500}{3} = \frac{498}{3}+\frac{1}{3}=166+\frac{1}{3}$$ miles
D
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
##### General Discussion
Manager
Joined: 02 Sep 2012
Posts: 182
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

16 Apr 2013, 07:18
hi,
how come your interpreting that train will meet by 300/9 hours? i a not getting it?can you explain?
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 584
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

Updated on: 16 Apr 2013, 08:32
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

Many ways to do this problem. However, the given speeds are 50 mph and 40 mph. Had the speeds been equal, both would have covered the exact same distance = 150 miles. However, as the speed of train A is a little more than train B, it would cover a little more than 150 miles, and a safe ballparking would lead to the answer of 167 miles.This method is only possible if the options are not spaced that closely.

Another way of doing this sum is : As the trains meet, the time taken is the same and hence constant for both. Thus, Da/50 = (300-Da)/40--> Da = 1500/9 = 1500*0.11 = 165 approx.

D.
_________________

Originally posted by mau5 on 16 Apr 2013, 07:20.
Last edited by mau5 on 16 Apr 2013, 08:32, edited 1 time in total.
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1013
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

16 Apr 2013, 07:26
Train A travels at 50 m/h, train B travels at 40 m/h. There is a distance of 300 m between them.

To find out when whey will meet there is a simple method: imagine a train that travels at a speed equal to the sum of the speed of the single trains.

In this way you obtain a train that travels at 90 m/h, and that will cover 300 miles in 300/9 hours.
300 miles will be covered by a train that travels at 50 + a train that travels at 40 in 300/9 h: the value you'll obtain is when the trains will meet.

Check this: http://gmatclub.com/blog/2010/10/%E2%80 ... -questions.
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Intern
Joined: 11 Apr 2011
Posts: 43
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

16 Apr 2013, 07:47
skamal7 wrote:
hi,
how come your interpreting that train will meet by 300/9 hours? i a not getting it?can you explain?

Since we know the distance (300) and the combined rate (90), we plug it into the formula:

Distance = Rate * Time
300 = 90 * Time

We can solve for the time they will meet cause we added the rate of Train A and Train B together.

So the time will be 300/90 from dividing 90 on both sides to isolate Time in the equation above.

Time will be 3.33 hours so now you can plug that in for Train A’s distance.

Distance = Rate * Time
Distance = 50 * 3.33
Distance = 166.5 or 167 according to answer choice D.
Manager
Joined: 26 Feb 2012
Posts: 88
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

18 Aug 2013, 08:00
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

Moving towards each other so relative speed is the sum of theirs rates i.e 50+40=90mph.
So time taken to meet T=D/relative speed= 300/90=>10/3
Thus A has traveled D=R*T=> 50*10/3(time they will meet)=>167 appox

Rgds
Prasannajeet
Senior Manager
Joined: 10 Jul 2013
Posts: 282
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

18 Aug 2013, 13:10
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

300 = 50t + 40t
or, t = 10/3.

so, Sa = 500/3 = 166.6666666 = 167
_________________
Asif vai.....
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

30 Sep 2014, 01:27
2
Lets say train A has travelled distance d when it met train B; it means train B has travelled distance (300-d)

Time taken by train A = time taken by train B (To meet at the crossover)

Setting up the equation

$$\frac{d}{50} = \frac{300-d}{40}$$

d = 166.666

_________________
Kindly press "+1 Kudos" to appreciate
VP
Joined: 07 Dec 2014
Posts: 1221
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

12 Jun 2016, 12:33
5/9*300=167 miles
Intern
Joined: 25 Jun 2015
Posts: 8
Location: Portugal
GMAT 1: 370 Q37 V37
GPA: 2.92
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

05 Aug 2016, 04:48
I did this way:
Train A Train B
50m/hr 40m/hr
100m/hr. 80m/hr
150m/hr. 120m/hr
200m/hr. 160m/hr +- 167 in between
250m/hr. 200m/hr
Director
Joined: 12 Nov 2016
Posts: 695
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

15 May 2017, 14:12
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

This problem deals with traveling entities , or simply trains, from opposite ends- there two premises to remember for a problem of this nature (i.e vehicles traveling from opposite ends)

1). Because they both start at the same time "start simultaneously" the amount of time they will have traveled for when they meet must be the same

In other words if 50 (t) + 40 (t) = 300 - time is a fixed variable in this problem

2). The total distance traveled by both vehicles must equal the sum of the individual distances traveled by both

so if A travels 50 miles and B travels 40 miles then the total distance must be 90 miles

90 (t) = 300
t = 3 1/3

50 (3 1/3) = 167 approx
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8456
Location: United States (CA)
Re: Trains A and B start simultaneously from stations 300 miles  [#permalink]

### Show Tags

16 Feb 2018, 10:44
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

We can let time of trains A and B = t and create the following equation:

50t + 40t = 300

90t = 300

t = 300/90 = 10/3 hours

So train A will have traveled 50 x 10/3= 500/3 = 166 2/3 miles by the time they passed, which is closest to the answer of 167.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Trains A and B start simultaneously from stations 300 miles   [#permalink] 16 Feb 2018, 10:44
Display posts from previous: Sort by