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

 It is currently 21 Oct 2019, 05:38

### 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

# Two cars are traveling on a highway in the same direction. If car A

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

### Hide Tags

Intern
Joined: 24 May 2018
Posts: 5
Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

Updated on: 07 Sep 2018, 18:17
1
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:44) correct 33% (01:56) wrong based on 85 sessions

### HideShow timer Statistics

Two cars are traveling on a highway in the same direction. If car A traveling at a rate of 55 mph is 18 miles ahead of car B, which is traveling at 45 mph, how much time will it take for car A to double the distance between itself and car B?

A) 1 hour and 48 mins
B) 3 hours
C) 3 hours and 36 mins
D) 4 hours
E) 4 hours and 18 mins

Originally posted by jennysussna on 07 Sep 2018, 13:28.
Last edited by generis on 07 Sep 2018, 18:17, edited 1 time in total.
Edited and formatted the question, renamed the topic
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

07 Sep 2018, 15:24
jennysussna wrote:
Two cars are traveling on a highway in the same direction. if car A traveling at a rate of 55mph is 18 miles ahead of car B, which is traveling at 45 mph, how muh time will it take for car a to double the distance between itself and car b?

a 1 hour and 48 mins
b 3 hours
c 3 hours and 36 mins
d 4 hours
e 4 hours and 18 mins

This problem is almost equal to the one you have posted here:
https://gmatclub.com/forum/ps-same-dist ... l#p2127282

That´s why I will allow myself to answer this one more briefly (as I would do in the real test):

(See figure attached.)

B is virtually not-moving,
A is virtually with 10mph and (FOCUS) must travel another 18 miles (therefore it will be 2*18 miles ahead of A)...

Remember: virtual time = real time (our FOCUS), hence:

$$? = 18\,\,{\text{miles}}\,\,\left( {\frac{{1\,\,{\text{h}}}}{{10\,\,{\text{miles}}}}} \right)\,\,\, = \,\,\frac{{5 + 4}}{5}\,\,{\text{h}}\,\,{\text{ = }}\,\,1{\text{h}}\,\,{\text{ + }}\,\,\frac{4}{5}{\text{h}}\,\,\left( {\frac{{60\,\,\min }}{{1\,\,\,{\text{h}}}}} \right) = 1{\text{h}}48\min$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Attachments

07Set18_9y.gif [ 3.55 KiB | Viewed 1333 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Senior SC Moderator
Joined: 22 May 2016
Posts: 3565
Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

07 Sep 2018, 17:38
1
jennysussna wrote:
Two cars are traveling on a highway in the same direction. if car A traveling at a rate of 55mph is 18 miles ahead of car B, which is traveling at 45 mph, how muh time will it take for car a to double the distance between itself and car b?

a 1 hour and 48 mins
b 3 hours
c 3 hours and 36 mins
d 4 hours
e 4 hours and 18 mins

This is a "runaway" problem with a "gap" and a trap (gap distance that Car A must travel is not 36 miles).

Use RT=D and "solve for the gap."
We need
1) the rate at which the gap widens ("relative speed")
2) gap distance

(1) Rate = relative speed. Travel is in SAME direction. Subtract slower speed from faster. Relative speed: $$(Rate_{A}-Rate_{B})=(55-45)=10mph$$

(2) Gap distance?
The gap distance at start: 18 miles
Desired gap distance? (18*2) = 36 miles
Car A is faster than B and ahead of car B.
The 18-mile distance between them never shrinks. Rather, that gap increases slowly.

Car A needs to get (36-18) = 18 ADDITIONAL miles ahead of Car B
$$D_{gap}=18$$ miles

(3) TIME required?
How long will it take for Car A to put another 18 miles between A and B?

Relative speed, $$R=10$$ mph
Distance of gap, $$D=18$$ miles
Time needed: $$RT=D$$, so $$T=\frac{D}{R}$$
$$T=\frac{18}{10}=\frac{9}{5}=1\frac{4}{5}$$ hours

Multiply any fraction of an hour by 60 to get minutes: $$(\frac{4}{5}*60)=48$$ minutes

Time needed: 1 hour, 48 minutes

ANSWER A

Check. From the time that A was 18 miles ahead of B to the time that A was 36 miles ahead of B, both cars traveled for $$\frac{9}{5}$$ hours.

Start: Car B was at the 0 mile mark
RT=D, so Car B traveled $$45*\frac{9}{5}=81$$ miles
End: Car B is at the 81-mile mark

Start: Car A started at the 18-mile mark
Car A traveled $$55*\frac{9}{5}=99$$ miles
End: Car A is at mile marker (18+99) = 117

Distance between A and B? (117-81)=36 mi

That works.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Intern
Joined: 09 Mar 2017
Posts: 12
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

23 Feb 2019, 08:17
What's the source of this question?
Manager
Joined: 09 Nov 2015
Posts: 136
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

23 Feb 2019, 23:28
Car A is 10 mph faster than Car B so it gains 10 miles in 1 hour on Car B. In order to double the distance the distance between them, Car A will have to gain 18 miles on Car B to do which it will need 18/10=1.8 hours=1 hr 48 mins. Ans: A.
Manager
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

24 Feb 2019, 00:56
here relative speed = 55-45 = 10 mph

current distance = 18
target distance = 36
required extra distance=18

It means we have to calculate how much time it will take to cover 18 miles with relative speed of 10 mph

time = 18/10 = 1.8 hours

so 1 hour and 48 mins

Posted from my mobile device
_________________
Ankit
GMAT is tough so I am ...
Giving Kudos is the best way to encourage and appreciate people
Intern
Joined: 28 Apr 2016
Posts: 16
Re: Two cars are traveling on a highway in the same direction. If car A  [#permalink]

### Show Tags

24 Feb 2019, 02:35
Relative speed is 10 mph, to cover 18 miles it would take a bit less than 2 hours, Only option A is less than 2 hours, hence is the correct answer.
Nice to go through the options before going into the calculations.
Re: Two cars are traveling on a highway in the same direction. If car A   [#permalink] 24 Feb 2019, 02:35
Display posts from previous: Sort by

# Two cars are traveling on a highway in the same direction. If car A

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne