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

Question

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:
https://magoosh.com/gmat/2014/gmat-pract ... on-motion/

Mike :-)

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Official Answer

B

vietnammba · Accepted Answer

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.

Van4ez · Answer

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

warriorguy · Answer

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

Blackbox · Answer

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 · Answer

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 · Answer

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!

mikemcgarry · 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

Blackbox · Answer

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.

connectvinoth · Answer

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

Posted from my mobile device

Mahmud6 · Answer

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.

Tanvi94 · Answer

when you say 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. Can you please explain why we shouldn't subtract as they are travelling in opposite directions?

HarshavardhanR · Answer

Hi Tanvi94 , I sense that you are not aware of where this concept of "adding the velocities if in opposite direction" and "subtracting the velocities if in the same direction" is coming from. Perhaps this will help. https://gmatclub.com/forum/download/file.php?id=82554 Observe the diagram. - Initially, P and Q are at A and B respectively. - They move in oppposite directions and meet at point R after time t1. - The distance travelled by P + the distance traveled by Q = AB = 120. - Using D = st, this gives us 49t1 + 61t1 = 120. Thus t1 = 120/(49+61). This is actually why we are "adding the two velocities when they move in the opposite direction". This is the rationale behind the relative velocity formula. - Similarly, from R, Q moves to C and P moves to D by time t2 such that the gap between them is 45 miles. - Again, Total Distance covered by both CD = RC + RD = 61t2 + 49t2 = t2(61+49) = 45. Thus t2 = 45/(49+61). Observe again that when the two bodies are moving in opposite directions, velocities end up getting added up. This is the actual derivation behind it. Hope this helps. ___ Harsha Passionate about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com GMAT-Club-Forum-a3d1u890.png

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

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