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

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

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21 Nov 2014, 16:13
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25% (medium)

Question Stats:

74% (01:51) correct 26% (02:01) wrong based on 224 sessions

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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

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Mike McGarry
Magoosh Test Prep

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

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21 Nov 2014, 22:59
2
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.
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Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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22 Nov 2014, 02:52
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
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Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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07 Oct 2016, 03:19
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
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Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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24 Sep 2017, 11:34
2
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?
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Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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24 Sep 2017, 13:43
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?

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

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24 Sep 2017, 15:36
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!
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680
Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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25 Sep 2017, 13:24
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

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

Manager
Joined: 30 May 2012
Posts: 217
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
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Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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25 Sep 2017, 14:21
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.
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Re: Cars P & Q are approaching each other on the same highway. Car P is m [#permalink]

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28 Sep 2017, 06:54
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.

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

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02 Feb 2018, 22:55
For relative speed of bodies moving in opposite direction, the equation is (Sp + Sq) X t = Distance

Here, total distance need to be covered is 120+45=165 miles

So, the equation becomes $$(49+61)t=165=>t=1.5$$ hours

2:00 pm +1.5 hours=3:30 pm.
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Cars P & Q are approaching each other on the same highway. Car P is m   [#permalink] 02 Feb 2018, 22:55
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