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Machines A and B both shrink-wrap CDs continuously, each working at a

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Bunuel
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Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink] New post   09 Jul 2021, 05:15
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Machines A and B both shrink-wrap CDs continuously, each working at a constant rate, but Machine B works 50% faster than Machine A. If Machine B shrink-wraps 48,000 more CDs in a 24-hour period than Machine A does, what is Machine A’s shrink-wrapping rate in CDs per hour?

(A) 4,000
(B) 6,000
(C) 8,000
(D) 12,000
(E) 16,000
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Re: Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink] New post   09 Jul 2021, 06:54
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Let the rate of Machine A be 2y CDs/Hr
Therefore, the rate of Machine B is 3y CDs/Hr (Since Machine B is 50% faster than Machine A)

In 24 Hrs,
Machine A shrink-wraps = (2y)x24= 48y CDs
Machine B shrink-wraps = (3y)x24= 72y CDs
Therefore, 72y-48y=48000
24y=48000
y=2000

Since, rate of Machine A is 2y = 2(2000) = 4000 CDs/hr
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Re: Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink] New post   14 Jul 2021, 06:16
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Let the rate of Machine A be x units per hour

then, the rate of Machine B will be 1.5x per hour

Their rate of work for 24 hours

Machine A = 24x
Machine B = 24* 1.5x = 36x

We are given the difference of their rate for 24 hours

Hence,

36x - 24x = 48000
12x = 48000
x = 4000

Answer option A
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Re: Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink] New post   06 Oct 2022, 01:11
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Bunuel wrote:
Machines A and B both shrink-wrap CDs continuously, each working at a constant rate, but Machine B works 50% faster than Machine A. If Machine B shrink-wraps 48,000 more CDs in a 24-hour period than Machine A does, what is Machine A’s shrink-wrapping rate in CDs per hour?

(A) 4,000
(B) 6,000
(C) 8,000
(D) 12,000
(E) 16,000

Solution:

  • Let us assume rate of machine A be \(r\). Then the rate of machine B will be \(1.5r\) (50% more than machine A)
  • We can make the WRT table as:
Attachment:
machinework.png
machinework.png [ 4.62 KiB | Viewed 2924 times ]

  • According to the question, \(36r-24r=48000\)
    \(⇒12r=48000\)
    \(⇒r=\frac{48000}{12}\)
    \(⇒r=4000\)

Hence the right answer is Option A
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Re: Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink] New post   17 Nov 2023, 13:42
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1.5x – x = 48000 therefore x = 96,000 units
Rate of Machine A = 96000 / 24 = 4,000 units per hr.
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Re: Machines A and B both shrink-wrap CDs continuously, each working at a [#permalink]
17 Nov 2023, 13:42
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