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Machine A can make 200 widgets in 14 hours, Machine B can make 200

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Machine A can make 200 widgets in 14 hours, Machine B can make 200 [#permalink]

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New post 26 Sep 2016, 09:46
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Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

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Re: Machine A can make 200 widgets in 14 hours, Machine B can make 200 [#permalink]

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New post 26 Sep 2016, 10:11
Nevernevergiveup wrote:
Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes


When working together A, B and C would take \(1/\frac{1}{(14} + \frac{1}{7} + \frac{1}{2})\) time to produce 200 widgets, which is \(\frac{14}{10}\), so to make 100, it takes \(\frac{1}{2}\) that time, \(\frac{7}{10} = 42 mins\)
Answer is B
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Re: Machine A can make 200 widgets in 14 hours, Machine B can make 200 [#permalink]

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New post 26 Sep 2016, 10:28
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This post was
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Nevernevergiveup wrote:
Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes


Efficiency of A = \(\frac{200}{14}\) Or \(\frac{100}{7}\) \(\frac{Units}{Hour}\)

Efficiency of B = \(\frac{200}{7}\) \(\frac{Units}{Hour}\)

Efficiency of C = 200/2 Or \(100\) \(\frac{Units}{Hour}\)

Combined efficiency of A , B and C is ( \(\frac{100}{7}\) + \(\frac{200}{7}\) + \(100\)) \(\frac{Units}{Hour}\) = \(\frac{1000}{7}\)

So, Time required to complete 100 units is 100/(1000/7) Hours

Or, 100 x 7/1000 x 60 minutes = 42 Minutes

Hence correct answer will be (B) 42 Minutes...

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Re: Machine A can make 200 widgets in 14 hours, Machine B can make 200 [#permalink]

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New post 13 May 2018, 07:15
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Machine A can make 200 widgets in 14 hours, Machine B can make 200   [#permalink] 13 May 2018, 07:15
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