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MGMAT Circles

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CoIIegeGrad09
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MGMAT Circles [#permalink] New post   06 Feb 2010, 19:17
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I've read the solution given by MGMAT..and it seemed pretty long. Does anyone know a way to do this problem quickly?

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?

4*– 1.6
4* + 8.4
4* + 10.4
2* – 1.6
2* – 0.8

NOTE: * means Pie (3.14). I have no idea how to insert a pie symbol...I apologize in advance.



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Re: MGMAT Circles [#permalink] New post   06 Feb 2010, 21:17
Here is how I have approached it:

the cars travelling along the circumference of the circle with radius 10. So distance is 2*10*pi=20*pi.
After 10 hours the distance beetween Car A and Car B is 20*pi-2mph*10h=20*pi-20
Time it takes for Car B and Car A to meet at the point is 10+(20*pi-20)/5=4*pi +6
To find the time it takes for the distance between Car A and Car B to reach 12 is equal to 12/5=2.4
So the total time is 4*pi +6+2.4= 4*pi +8.4

*=multiply
pi=3.14
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 06:23
A

I have quickly worked out the answer, but first I need to know whether my answer is right.
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 07:00
aniec, do you take into account first 10 hours that Car B travels?
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 08:37
alexBLR wrote:
aniec, do you take into account first 10 hours that Car B travels?



No, I don't. The question ask" For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?" Car B haven't travelled at the first 10 hours.
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 10:06
aniec wrote:
alexBLR wrote:
aniec, do you take into account first 10 hours that Car B travels?



No, I don't. The question ask" For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?" Car B haven't travelled at the first 10 hours.



aniec, read the problem statement carefully, the Car A didn't travel first 10 hours, Car B did
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 10:14
CoIIegeGrad09 , please provide OA.
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 19:13
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I agree with Alex that the answer is B.

1. Car B is \(20\pi -20\) miles away when car A starts moving ten hours later.

2. When Car A starts moving they are moving toward each other at a net speed of 5 mph (5t). Time until they meet:

\(20\pi - 20 = 5t\)

\(t = 4\pi - 4\)

3. When they meet they now need to move 12 miles apart at a net speed of 5mph:

\(5t = 12\) so \(t = \frac{12}{5}\)

4. Combine all of the t values together. 10 hours + time to meet + time to move away 12 miles.

\(10 + 4\pi - 4 + \frac{12}{5} = 4\pi + 8.4\)
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Re: MGMAT Circles [#permalink] New post   07 Feb 2010, 22:01
alexBLR wrote:
aniec wrote:
alexBLR wrote:
aniec, do you take into account first 10 hours that Car B travels?



No, I don't. The question ask" For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?" Car B haven't travelled at the first 10 hours.



aniec, read the problem statement carefully, the Car A didn't travel first 10 hours, Car B did



Sorry, then the answer is B.

(20pi-20+12)/(2+3)+10



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Re: MGMAT Circles [#permalink]
07 Feb 2010, 22:01
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