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Two circles, one with radius 10 inches and the other with radius 4

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GeminiHeat
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Two circles, one with radius 10 inches and the other with radius 4 [#permalink] New post   26 Apr 2021, 07:23
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Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point Q. Two insects start crawling at the same time from point Q: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point Q?

(A) 15 minutes

(B) 30 minutes

(C) 40 minutes

(D) 1 hour

(E) 1 hour, 20 minutes
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nurakib
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Re: Two circles, one with radius 10 inches and the other with radius 4 [#permalink] New post   27 Apr 2021, 05:35
Is it B?
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Re: Two circles, one with radius 10 inches and the other with radius 4 [#permalink] New post   27 Apr 2021, 09:56
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GeminiHeat wrote:
Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point Q. Two insects start crawling at the same time from point Q: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point Q?

(A) 15 minutes

(B) 30 minutes

(C) 40 minutes

(D) 1 hour

(E) 1 hour, 20 minutes


Distance to be covered on larger circle = 2π(10) = 20π
Distance to be covered on smaller circle = 2π(4) = 8π

Since, both the insects have to be back at point Q, we must take the LCM of these distances i.e. 40π

Now, the relative speed between these two insects = 3π - 2.5π = 0.5π

Time = \frac{40π}{0.5π} = 80 minutes i.e. 1 hour 20 minutes

Hence, option E
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Re: Two circles, one with radius 10 inches and the other with radius 4 [#permalink] New post   07 Nov 2023, 15:58
Hello from the GRE Prep Club BumpBot!

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Re: Two circles, one with radius 10 inches and the other with radius 4 [#permalink]
07 Nov 2023, 15:58
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