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# GRE Math Challenge #90-A certain machine drills 30 holes

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GRE Math Challenge #90-A certain machine drills 30 holes [#permalink]  09 May 2015, 11:32
Expert's post
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Question Stats:

85% (00:56) correct 14% (00:47) wrong based on 7 sessions
A certain machine drills 30 holes in 8 minutes. At that constant rate, how many holes will 4 such machines drill in $$1\frac{1}{3}$$ hours?

(A) 300
(B) 900
(C) 960
(D) 1,200
(E) 2,560
[Reveal] Spoiler: OA
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Re: GRE Math Challenge #90-A certain machine drills 30 holes [#permalink]  17 Dec 2017, 21:52
1
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sandy wrote:
A certain machine drills 30 holes in 8 minutes. At that constant rate, how many holes will 4 such machines drill in $$1\frac{1}{3}$$ hours?

(A) 300
(B) 900
(C) 960
(D) 1,200
(E) 2,560

Here $$1\frac{1}{3}$$ = 80minutes

Therefore we KNow-

Amount of work = Rate * Time

Amount of work = 30 holes

Rate = we need to find it

Time = 8 minutes

No. of machine = 1

so in first case

30 = 1 * R * 8
or Rate= $$\frac{30}{8}$$

Now for the 2nd case

Amount of work = We need to find out

Rate = $$\frac{30}{8}$$

No. of machine = 4

Time = 80 minutes

Therefore

A =R * T

A = 4 * $$\frac{30}{8}$$ * 80

or A = 1200 holes
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Re: GRE Math Challenge #90-A certain machine drills 30 holes [#permalink]  18 Dec 2017, 02:26
1
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We know the following formula :
# of outputs = (Rate)(Time)(# of machines)
We know that the outputs are 30 holes, time is 8 minutes and number of machine is 1.
Lets plug this
30 = (Rate)(8)(1)
Therefore the rate is 3,75 holes in one minute.
Now we are asking to find the number of outputs done by 4 machines in 1(1/3) hour.
Lets convert 1(1/3) this equals to 1h 20 minutes of 80 minutes.
Lets use again the same formula
# of outputs = (rate)(time)(# of machines)
# of outputs = (3,75)(80)(4)
# of outputs = 1200
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Re: GRE Math Challenge #90-A certain machine drills 30 holes [#permalink]  16 May 2018, 09:22
1
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Expert's post
sandy wrote:
A certain machine drills 30 holes in 8 minutes. At that constant rate, how many holes will 4 such machines drill in $$1\frac{1}{3}$$ hours?

(A) 300
(B) 900
(C) 960
(D) 1,200
(E) 2,560

The rate of one machine is 30/8 = 15/4 holes per minute, so the rate of 4 machines is 4 x 15/4 = 15 holes per minute. Since 1 1/3 hours = 80 minutes, the 4 machines can drill 15 x 80 = 1200 holes.

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Re: GRE Math Challenge #90-A certain machine drills 30 holes   [#permalink] 16 May 2018, 09:22
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