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Two circles, one with radius 10 inches and the other with radius 4
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26 Apr 2021, 07:23
26 Apr 2021, 07:23
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Question Stats:
45% (02:35) correct
54% (03:05) wrong based on 37 sessions
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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
(A) 15 minutes
(B) 30 minutes
(C) 40 minutes
(D) 1 hour
(E) 1 hour, 20 minutes
Re: Two circles, one with radius 10 inches and the other with radius 4
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27 Apr 2021, 05:35
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
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27 Apr 2021, 09:56
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
(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
