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A certain machine drills 30 holes in 8 minutes. At that constant rate,

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A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 15 May 2018, 02:45
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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

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A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post Updated on: 16 May 2018, 10:56
1 machine drills 30 holes in 8 minutes
1 machine drills 300 holes in 80 minutes. 80 minutes = \(1\frac{1}{3}\) hours
4 machines drill 300*4 = 1200 holes in 80 minutes

Hence option D = 1200 is the answer.
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Originally posted by houston1980 on 15 May 2018, 02:50.
Last edited by houston1980 on 16 May 2018, 10:56, edited 1 time in total.
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 15 May 2018, 02:57
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Rate of one machine is \(\frac{(30 holes)}{(8 mins)}\)

therefore, Rate of 4 machines is \(\frac{4 * (30 holes)}{(8 min)}\)
= \(\frac{15 holes}{min}\)

therefore total number of holes in \(\frac{4}{3} *60 mins\)

= \(15 * 80\)

= 1200

Answer is D
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 15 May 2018, 03:35

Solution



Given:
• 1 machine drills 30 holes in 8 minutes

To find:
• How many holes will 4 such machines drill in 1\(\frac{1}{3}\) hrs (= \(\frac{4}{3}\) hrs = 80 minutes)

Approach and Working:
• 1 machine in 8 minutes drill 30 holes
    Or, 1 machine in 1-minute drill \(30*\frac{1}{8}\) holes
    Or, 4 machines in 1-minute drill \(30*\frac{1}{8}*4\) holes
    Or, 4 machines in 80 minutes drill \(30*\frac{1}{8}*4*80\) holes = 1200 holes
Hence, the correct answer is option D.

Answer: D
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 15 May 2018, 03:37
Bunuel 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


First of, \(1\frac{1}{3}\) = 60 + 1/3*60 = 80 minutes

1 machine ---- 8 minutes ------ 30 holes (Rate = 30/8 holes per minute)

4 machines ------ 80 minutes ------ 30/8*80*4 holes

1200 (D)

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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 15 May 2018, 03:43
1 M drills 30 holes in 8 minutes
1 M will drills 300 holes in 80 minutes.
4 M will drill 300*4 = 1200 holes in 80 minutes

1200
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 16 May 2018, 10:51
Bunuel 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.

Answer: D
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate,  [#permalink]

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New post 03 Oct 2018, 01:07
A machine drills hole per min= 30/8 (holes/min)
In 4/3 hours= 80 mins=30*80/8= 300 holes

So, 4 machines drill holes in 4/3 hrs= 300*4= 1200 holes

(D)
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Re: A certain machine drills 30 holes in 8 minutes. At that constant rate, &nbs [#permalink] 03 Oct 2018, 01:07
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