It is currently 19 Nov 2017, 03:13

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Cars P & Q are approaching each other on the same highway. Car P is m

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

Hide Tags

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488

Kudos [?]: 8738 [0], given: 105

Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 21 Nov 2014, 17:13
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:47) correct 26% (01:54) wrong based on 179 sessions

HideShow timer Statistics

Cars P & Q are approaching each other on the same highway. Car P is moving at 49 mph northbound and Car Q is moving at 61 mph southbound. At 2:00 pm, they are approaching each other and 120 mi apart. Eventually they pass each other. At what clock time are they moving away from each other and 45 miles apart?
(A) 3:06 pm
(B) 3:30 pm
(C) 3:54 pm
(D) 5:21 pm
(E) 6:15 pm


For a set of practice problems on Motion, including the OE for this particular problem, see:
http://magoosh.com/gmat/2014/gmat-pract ... on-motion/

Mike :-)
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8738 [0], given: 105

Magoosh Discount CodesOptimus Prep Discount CodesEconomist GMAT Tutor Discount Codes
2 KUDOS received
Intern
Intern
User avatar
Joined: 25 Jun 2014
Posts: 46

Kudos [?]: 23 [2], given: 187

Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 21 Nov 2014, 23:59
2
This post received
KUDOS
The time they pass each other and 45 miles apart, they cover totally 120m + 45m = total 165 mile.
The time they need is: total distance/49 + 61 = 1,5h
=> The time is 3h30
Btw, I love your blog and I learned alot from your verbal section. Thank you so much.

Kudos [?]: 23 [2], given: 187

Current Student
avatar
Joined: 27 Oct 2014
Posts: 23

Kudos [?]: 7 [0], given: 66

GMAT 1: 680 Q49 V34
GPA: 3.8
GMAT ToolKit User Reviews Badge
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 22 Nov 2014, 03:52
The answer is B
Total distance, which should be covered by both cars is 120+45=165 miles. Let x be the time so the equation will be 49x+61x=165 and x=1.5 hours

Kudos [?]: 7 [0], given: 66

Chat Moderator
avatar
G
Joined: 04 Aug 2016
Posts: 589

Kudos [?]: 92 [0], given: 140

Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)
Premium Member CAT Tests
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 07 Oct 2016, 04:19
Car P is moving at 49 mph northbound and Car P is moving at 61 mph southbound


Shouldn't it be Car P and Car Q? :D

Kudos [?]: 92 [0], given: 140

1 KUDOS received
Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [1], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 24 Sep 2017, 12:34
1
This post received
KUDOS
mikemcgarry,

Please correct my approach if need be.

Given that the objects are traveling in opposite directions. So, add their individual speeds.

Total Speed = 110mph
Distance between objects = 120 mi
Time = D/T => 120/110 = 12/11 = 1hr 9 mins (approx.)

Therefore, relative to the time when those objects began their travel, they will cross each other at approx 3:09pm

Now, it is also given that once they cross paths, they travel for another 45 mi. Prompt's asking how long it took to travel 45 mi away from each other.

We know their combined speed is 110 mph, distance is 45mi. So, calculate time taken to scale 45mi.

T = 45/110
T = 0.40 hrs (approx.) which is 24 minutes (approx.)

Therefore, adding these 24 mins to 3:09pm, the final result will be 3:33pm, which is B.

Is this approach OK?

Kudos [?]: 82 [1], given: 151

Manager
Manager
User avatar
B
Joined: 13 Oct 2013
Posts: 134

Kudos [?]: 57 [0], given: 129

Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 24 Sep 2017, 14:43
Hello Blackbox,

i also solved in same way as you did. But i took relative velocity 12 (61-49) as they move in opposite direction for 45 miles after they cross each other. but i did not get the correct answer.


Blackbox wrote:
mikemcgarry,

Please correct my approach if need be.

Given that the objects are traveling in opposite directions. So, add their individual speeds.

Total Speed = 110mph
Distance between objects = 120 mi
Time = D/T => 120/110 = 12/11 = 1hr 9 mins (approx.)

Therefore, relative to the time when those objects began their travel, they will cross each other at approx 3:09pm

Now, it is also given that once they cross paths, they travel for another 45 mi. Prompt's asking how long it took to travel 45 mi away from each other.

We know their combined speed is 110 mph, distance is 45mi. So, calculate time taken to scale 45mi.

T = 45/110
T = 0.40 hrs (approx.) which is 24 minutes (approx.)

Therefore, adding these 24 mins to 3:09pm, the final result will be 3:33pm, which is B.

Is this approach OK?

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Kudos [?]: 57 [0], given: 129

Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [0], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 24 Sep 2017, 16:36
sunita123 - I wish I could help! This topic (when two objects travel at different speeds relative to each other) is confusing to me and I think Magoosh folks did a good job at explaining this- Add the two objects' individual speeds when they are traveling towards or away from each other. Subtract when they traveling along the same path). Therefore, I really don't know how to calculate with relative speed approach. Sorry!

Kudos [?]: 82 [0], given: 151

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488

Kudos [?]: 8738 [0], given: 105

Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 25 Sep 2017, 14:24
Blackbox wrote:
mikemcgarry,

Please correct my approach if need be.

Given that the objects are traveling in opposite directions. So, add their individual speeds.

Total Speed = 110mph
Distance between objects = 120 mi
Time = D/T => 120/110 = 12/11 = 1hr 9 mins (approx.)

Therefore, relative to the time when those objects began their travel, they will cross each other at approx 3:09pm

Now, it is also given that once they cross paths, they travel for another 45 mi. Prompt's asking how long it took to travel 45 mi away from each other.

We know their combined speed is 110 mph, distance is 45mi. So, calculate time taken to scale 45mi.

T = 45/110
T = 0.40 hrs (approx.) which is 24 minutes (approx.)

Therefore, adding these 24 mins to 3:09pm, the final result will be 3:33pm, which is B.

Is this approach OK?

sunita123 wrote:
Hello Blackbox,

i also solved in same way as you did. But i took relative velocity 12 (61-49) as they move in opposite direction for 45 miles after they cross each other. but i did not get the correct answer.

Dear Blackbox & sunita123,

I'm happy to respond. :-)

Blackbox, your approach was fine but was not the most efficient method. When the velocities are in opposite directions, we add the velocities, regardless of whether they are approaching head-on or receding in opposite directions. Thus, it is the same pattern for both distances in this problem, so we can just add the distances and divide by the sum of the speeds:
(120 + 45)/110 = 165/110 = 15*11/110 = 15/10 = 1.5 hr
That would be the most efficient method of solution.

sunita123, my friend, I'm sorry to say that you don't understand relative velocity. Once again, for relative velocity, you ADD if the velocities are in opposite direction and only SUBTRACT if the velocities are in the same direction. It's not a one-size-fits-all formula.

Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8738 [0], given: 105

Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [0], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 25 Sep 2017, 15:21
mikemcgarry wrote:
Blackbox wrote:
mikemcgarry,

Please correct my approach if need be.

Given that the objects are traveling in opposite directions. So, add their individual speeds.

Total Speed = 110mph
Distance between objects = 120 mi
Time = D/T => 120/110 = 12/11 = 1hr 9 mins (approx.)

Therefore, relative to the time when those objects began their travel, they will cross each other at approx 3:09pm

Now, it is also given that once they cross paths, they travel for another 45 mi. Prompt's asking how long it took to travel 45 mi away from each other.

We know their combined speed is 110 mph, distance is 45mi. So, calculate time taken to scale 45mi.

T = 45/110
T = 0.40 hrs (approx.) which is 24 minutes (approx.)

Therefore, adding these 24 mins to 3:09pm, the final result will be 3:33pm, which is B.

Is this approach OK?

sunita123 wrote:
Hello Blackbox,

i also solved in same way as you did. But i took relative velocity 12 (61-49) as they move in opposite direction for 45 miles after they cross each other. but i did not get the correct answer.

Dear Blackbox & sunita123,

I'm happy to respond. :-)

Blackbox, your approach was fine but was not the most efficient method. When the velocities are in opposite directions, we add the velocities, regardless of whether they are approaching head-on or receding in opposite directions. Thus, it is the same pattern for both distances in this problem, so we can just add the distances and divide by the sum of the speeds:
(120 + 45)/110 = 165/110 = 15*11/110 = 15/10 = 1.5 hr
That would be the most efficient method of solution.

sunita123, my friend, I'm sorry to say that you don't understand relative velocity. Once again, for relative velocity, you ADD if the velocities are in opposite direction and only SUBTRACT if the velocities are in the same direction. It's not a one-size-fits-all formula.

Does this make sense?
Mike :-)


mikemcgarry - Thank you, kind sir! I have been watching Magoosh videos and have so far not regretted buying the product. It has proved to be very efficient with Rate problems. I did not know you could also combine the distances if two objects are traveling towards each other. I wish there were a video with such a example. But, of course, I understand there are only so many tutorial videos that could be showcased. Nevertheless, I am loving Magoosh Math! Thank you again.

Kudos [?]: 82 [0], given: 151

Intern
Intern
avatar
B
Joined: 25 Mar 2012
Posts: 5

Kudos [?]: [0], given: 15

Concentration: Strategy, Leadership
Schools: NTU '16
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

Show Tags

New post 28 Sep 2017, 07:54
vietnammba wrote:
The time they pass each other and 45 miles apart, they cover totally 120m + 45m = total 165 mile.
The time they need is: total distance/49 + 61 = 1,5h
=> The time is 3h30
Btw, I love your blog and I learned alot from your verbal section. Thank you so much.


Good one. I Didn’t realise I can just sum the distance.

Posted from my mobile device

Kudos [?]: [0], given: 15

Re: Cars P & Q are approaching each other on the same highway. Car P is m   [#permalink] 28 Sep 2017, 07:54
Display posts from previous: Sort by

Cars P & Q are approaching each other on the same highway. Car P is m

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.