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Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Nov 2009, 01:34
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Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B? A. \(4\pi – 1.6\) B. \(4\pi + 8.4\) C. \(4\pi + 10.4\) D. \(2\pi – 1.6\) E. \(2\pi – 0.8\) The OA is pretty long and even solving it that way takes me +2 mins. Hopefully someone can offer a fast solution.
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Last edited by Bunuel on 17 Dec 2017, 00:11, edited 3 times in total.
Edited the question and added the OA



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Nov 2009, 02:10
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Alright, first of all, let's determine the distance of the circular track:
Circumference = pi*d = 20*pi
Now, let's represent each car's distance from the starting point (along the track), t hours from when Car A starts:
B(t) = 20 + 2t [Distance traveled after 10 hours, + 2mph) A(t) = 20*pi  3t [Starting at starting point (20pi), 3mph)
We need to determine the time it takes for car A to be 12 miles past car B.
B(t)  A(t) = 12 20 + 2t  (20*pi 3t) = 12 t = (8 + 20pi)/5 t = 4pi  1.6
Therefore, car A has been traveling (4pi  1.6) hours before the criterion is satisfied.The question, however, asks how long car B has been traveling.
t + 10 = 4pi  1.6 + 10 = 4pi + 8.4
Therefore the answer is B: 4pi + 8.4.



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Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?A. \(4\pi – 1.6\) B. \(4\pi + 8.4\) C. \(4\pi + 10.4\) D. \(2\pi – 1.6\) E. \(2\pi – 0.8\) It's possible to write the whole formula right away but I think it would be better to go step by step: B speed: 2 mph; A speed: 3 mph (travelling in the opposite direction); Track distance: \(2*\pi*r=20*\pi\); What distance will cover B in 10h: \(10*2=20\) miles Distance between B and A by the time, A starts to travel: \(20*\pi20\) Time needed for A and B to meet distance between them divided by the relative speed: \(\frac{20*\pi20}{2+3}= \frac{20*\pi20}{5}=4*\pi4\), as they are travelling in opposite directions relative speed would be the sum of their rates; Time needed for A to be 12 miles ahead of B: \(\frac{12}{2+3}=2.4\); So we have three period of times: Time before A started travelling: 10 hours; Time for A and B to meet: \(4*\pi4\) hours; Time needed for A to be 12 miles ahead of B: 2.4 hours; Total time: \(10+4*\pi4+2.4=4*\pi+8.4\) hours. Answer: B.
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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Nov 2009, 02:54
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Where I am going wrong? Please tell me
The total distance the cars need to travel at relative speed of 2+3=5 mph is 2piX1020 + 12 miles time required is (2piX10 20 + 12)/5 = 4pi 1.6 Answer  A



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Nov 2009, 03:13



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Nov 2009, 03:28
Thanks a lot Bunuel. I must learn to read the question properly. The answer is B.



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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17 Nov 2009, 12:59
Also, instead of using "pi" just use "3" and multiply. Instead of 20pi the track is 20*3= 60 miles, and the total time for B will be 20.4 = 4pi +8.4



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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19 Sep 2010, 02:19
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Solved the equation (20pi20)3t2t=12, but forgot to add the first 10 hours as well, so I got A at first.



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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01 Oct 2010, 08:36
I also forgot to add the first 10 hours =). To reckognize all the details is sooo important!!!!



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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10 Jan 2011, 18:48
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1. Circumference = 2(pi)r = 2(pi)10 = 20(pi) 2. Car B travels for 10 hours @ 2 miles = 20 miles 3. Car A starts at same location but travels counter clock wise (so A and B approaching each other = add speed) 4. Distance [Remaining] between two cars [when car A starts] = 20(pi) [total]  20 [traveled by B] 5. cars need to travel additional 12 miles so total distance to travel is 20(pi)  20 + 12 6. time = distance / speed = (20(pi)8) / 5 = 4(pi)  1.6 7. We have been asked to find how much time car B is travelling = 10 + 4(pi)  1.6 = 4(pi) + 8.4
Hope This Helps



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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ajit257 wrote: Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counterclockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)? a.4pi – 1.6 b.4pi + 8.4 c.4pi + 10.4 d.2pi – 1.6 e. 2pi – 0.8
did not get this one. Make the diagram. You will be able to see how to solve it. Attachment:
Ques1.jpg [ 16.63 KiB  Viewed 27339 times ]
Radius of track is 10 miles so circumference is 20*pi i.e. the total length of the track. B starts from X and travels for 10 hrs clockwise at 2 mph i.e. it travels 20 miles. Now car A starts from X counter clockwise. Distance between A and B is 20*pi  20. Now, to meet, they have to together cover this distance plus 12 miles more which they have to put between them. Time taken to cover this distance by them = (20*pi  20 + 12)/(3 + 2) = 4*pi  1.6 hrs Car B has been traveling for 10 + 4*pi  1.6 = (4*pi + 8.4) hrs
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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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11 Jan 2011, 20:30
VeritasPrepKarishma wrote: Radius of track is 10 miles so circumference is 20*pi i.e. the total length of the track. B starts from X and travels for 10 hrs clockwise at 2 mph i.e. it travels 20 miles. Now car A starts from X counter clockwise. Distance between A and B is 20*pi  20. Now, to meet, they have to together cover this distance plus 12 miles more which they have to put between them. Time taken to cover this distance by them = (20*pi  20 + 12)/(3 + 2) = 4*pi  1.6 hrs Car B has been traveling for 10 + 4*pi  1.6 = (4*pi + 8.4) hrs Hi Karishma, i actually got this question wrong when i took the mgmat cat last week, i got confused on the explanation which is similar to yours (your diagram helps though), how did you derive this equation: (20*pi  20 + 12)/(3 + 2), was this manipulated from Rate x Time = Distance? thanks.



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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gtr022001 wrote: VeritasPrepKarishma wrote: Radius of track is 10 miles so circumference is 20*pi i.e. the total length of the track. B starts from X and travels for 10 hrs clockwise at 2 mph i.e. it travels 20 miles. Now car A starts from X counter clockwise. Distance between A and B is 20*pi  20. Now, to meet, they have to together cover this distance plus 12 miles more which they have to put between them. Time taken to cover this distance by them = (20*pi  20 + 12)/(3 + 2) = 4*pi  1.6 hrs Car B has been traveling for 10 + 4*pi  1.6 = (4*pi + 8.4) hrs Hi Karishma, i actually got this question wrong when i took the mgmat cat last week, i got confused on the explanation which is similar to yours (your diagram helps though), how did you derive this equation: (20*pi  20 + 12)/(3 + 2), was this manipulated from Rate x Time = Distance? thanks. Attachment:
Ques1.jpg [ 14.88 KiB  Viewed 27185 times ]
The red distance is what B has already covered at 2 mph in 10 hrs. This distance is 20 miles. A and B are now moving towards each other (as shown by green arrows). To meet for the first time, they have to cover the remaining circumference of the track i.e. a distance of 20pi  20. (20pi is the circumference of the circle out of which 20 has already been covered by B). They need to create a further 12 miles distance between them. So together they need to cover (20pi  20 + 12) miles in all. Since, A and B are moving towards each other, their relative speed (i.e. combined speed here) will be (3 + 2) mph. So time taken for them to meet = D/S = (20pi  20 + 12)/(3 + 2)  Here, we are using the concept of Relative Speed. When two objects (speeds S1 and S2) move in opposite directions (towards each other or away from each other), they cover the distance between them (or create distance between them) at the rate of (S1 + S2). Here they are moving in opposite directions towards each other so their relative speed is sum of their speeds. After meeting, they are moving away from each other but their relative speed is still sum of their speeds. When two objects move in same direction, their speeds get subtracted. If this is unclear, I would suggest looking up the theory of relative speed for details.
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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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13 Jan 2011, 20:05
thank you Karishma for taking the time to explain this problem, i'll review a bit on relative speed since it is kind of new for me but your explanation is very helpful, as usual.



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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ok.
SO Since they are travelling in opposite directions then the sum of their individual distances should be equal to the total distance.
Therefore, Let T be the time they meet Distance travelled by A = 3x(t10), since it started 10 hours after B Distance travelled by B = 2xt,
Total distance =20Pi + 12
hence Distance of A + Distance of B=Total distance 2t+3(t10)=20pi+12 Solving..... 5t=20pi+42
t=4pi+8.4
the interesting thing is, the object which starts later, say "A", in this case is subtracted from time T by the number of hours it starts late. Thanks



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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14 Mar 2013, 11:56
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EASY EQUATION: I think the easy way to calculate is.
Distance travelled by B + Distance travelled by A = Circumference + 12 Let's sat the answer is T.
2T + 3(T10) = (2 * Pi * 10 )+ 12 5t = 20 pi + 42 t= 4 pi + 8.4



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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these type of ques can really come in gmat????? if v r not able to do these type of ques...how much it cud effect our scores ?



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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17 Mar 2013, 22:07
Perhaps wrote: these type of ques can really come in gmat????? if v r not able to do these type of ques...how much it cud effect our scores ? If you are hoping for a high Quant score then you can certainly come across such a question. The effect it will have on your score is the effect you let it have  if you put in 5 mins to solve it, do not still get it, guess on it and get all bogged down, it will have a big effect on your score. If you try to work it out for a couple of mins but are not able to so guess and move on and just take it in your stride, it will not have much impact. One question doesn't decide your score. But, if you already know that you don't know how to handle such questions, put in the effort to learn right now rather than worry in the test.
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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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Hi, Can u plz tell me where i am going wrong: Rate of Car B Rb=2mph,Ra=3mph time taken by car B = t+10 Time taken by A = t
since both will meet at some point,so they cover entire distance which is 20pi miles so equating: 2(t+10)= 3t t=20hrs so they meet in 20hrs time Now we need to check how much time B wouldve spent to cover the additional 12 miles. Its speed is 2mph so to cover 12miles it will take 6 hrs. How does pi come into the answer choices? Can u explain the correct approach using 20hrs meeting time as the starting point. Plz help.
Thanks, Shreeraj



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Re: Car B begins moving at 2 mph around a circular track with a radius of [#permalink]
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21 Mar 2013, 00:35
shreerajp99 wrote: Hi, Can u plz tell me where i am going wrong: Rate of Car B Rb=2mph,Ra=3mph time taken by car B = t+10 Time taken by A = t
since both will meet at some point,so they cover entire distance which is 20pi miles so equating: 2(t+10)= 3t
From where do you get this equation? You are assuming that the distances covered by them are equal. That is not the case. They together covered the entire circumference of the circle which is \(20\pi\). We can't say that they covered equal distances of \(10\pi\) each. Check the diagram and explanation given in my post above.
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