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To service a single device in 12 seconds, 700 nanorobots are

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sandy
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To service a single device in 12 seconds, 700 nanorobots are [#permalink] New post   18 Jun 2018, 14:51
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To service a single device in 12 seconds, 700 nanorobots are required, with all nanorobots
working at the same constant rate. How many hours would it take for a single nanorobot to service
12 devices?
(A) \(\frac{7}{3}\)
(B) 28
(C) 108
(D) 1,008
(E) 1,680
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Re: To service a single device in 12 seconds, 700 nanorobots are [#permalink] New post   28 Jun 2018, 17:09
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sandy wrote:
To service a single device in 12 seconds, 700 nanorobots are required, with all nanorobots
working at the same constant rate. How many hours would it take for a single nanorobot to service
12 devices?
(A) \(\frac{7}{3}\)
(B) 28
(C) 108
(D) 1,008
(E) 1,680


We know

Work = Rate * Time * No. of individual

In first to need to find out the rate

Given time = 12 seconds , No. of Individual = 700 nanorobots and Work = 1

Therefore; 1 = Rate * 12 * 700

or Rate = \(\frac{1}{8400}\)

Now for the second part we have

Work = 12 device, No. of Individual = 1 nanorobots and Rate = \(\frac{1}{8400}\)

Therefore; \(12 =\) \(\frac{1}{8400} * 1 * Time\)

or Time = 12 * 8400 = 100800 seconds = \(\frac{100800}{3600}\)hour = 28 hours
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Re: To service a single device in 12 seconds, 700 nanorobots are [#permalink] New post   10 Jul 2018, 05:24
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Explanation

To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:

Work = Individual Rate × Number of Workers × Time

Solve for an individual nanorobot’s rate, using the fact that 700 nanorobots can service 1 device in 12 seconds. Notice that the “work” here is 1 device:

Work = Individual Rate × Number of Workers × Time

1 device = (R)(700)(12 seconds)

R = \(\frac{1}{8400}\) devices per second.

That is, each nanorobot can service \(\frac{1}{8400}\) of a device in 1 second. Plug that rate back into the formula, but using the details from the second sentence in the problem:

Work = Individual Rate × Number of Workers × Time

12 devices = (\(\frac{1}{8400}\) devices per second)(1)(T)
T = 100,800 seconds

The answer is 100,800 seconds. Divide by 60 to convert this time to 1,680 minutes; divide by 60 again to get 28 hours.
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To service a single device in 12 seconds, 700 nanorobots are [#permalink] New post   27 Oct 2021, 09:57
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Individual nanorobot has speed 1/(12*700) to service one device

To service twelve devices, the required time in seconds is 12 divided by individual nanorobot's speed

12 : 1/(12*700) = 144*700 seconds

Hourly time is 144*700/3600 = 28 hours
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Re: To service a single device in 12 seconds, 700 nanorobots are [#permalink] New post   02 May 2025, 00:48
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Re: To service a single device in 12 seconds, 700 nanorobots are [#permalink]
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