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To service a single device in 12 seconds, 700 nanorobots are
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18 Jun 2018, 14:51
18 Jun 2018, 14:51
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69% (01:58) correct
30% (02:22) wrong based on 99 sessions
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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
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
Re: To service a single device in 12 seconds, 700 nanorobots are
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28 Jun 2018, 17:09
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
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
Re: To service a single device in 12 seconds, 700 nanorobots are
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10 Jul 2018, 05:24
10 Jul 2018, 05:24
Expert Reply
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.
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.
