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# Machine A can produce

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Machine A can produce [#permalink]  10 Sep 2019, 12:20
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99% (01:35) correct 0% (00:00) wrong based on 17 sessions
Machine A can produce $$\frac{1}{6}$$ of a ton of paintbrushes in one hour. Machine B can produce $$\frac{1}{14}$$ of a ton of paintbrushes in one hour. Working together at their individual rates, how long would it take the two machines to produce 2 tons of paintbrushes?

A. 8 hours

B. 8 hours 24 minutes

C. 9 hours

D. 9 hours 46 minutes

E. 12 hours

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Last edited by Carcass on 10 Sep 2019, 21:32, edited 1 time in total.
Fixed typo
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Re: Machine A can produce [#permalink]  11 Sep 2019, 04:58
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Carcass wrote:
Machine A can produce $$\frac{1}{6}$$ of a ton of paintbrushes in one hour. Machine B can produce $$\frac{1}{14}$$ of a ton of paintbrushes in one hour. Working together at their individual rates, how long would it take the two machines to produce 2 tons of paintbrushes?

A. 8 hours

B. 8 hours 24 minutes

C. 9 hours

D. 9 hours 46 minutes

E. 12 hours

Kudos for the right answer and explanation

Their COMBINED rate = 1/6 + 1/14 = 7/42 + 3/42 = 10/42 = 5/21 tons per hour

We want to make 2 tons

Time = output/rate
= 2/(5/21)
= (2)(21/5)
= 42/5
= 8 2/5 hours
= 8 hours 24 minutes

Cheers,
Brent
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Re: Machine A can produce [#permalink]  11 Sep 2019, 10:44
Carcass wrote:
Machine A can produce $$\frac{1}{6}$$ of a ton of paintbrushes in one hour. Machine B can produce $$\frac{1}{14}$$ of a ton of paintbrushes in one hour. Working together at their individual rates, how long would it take the two machines to produce 2 tons of paintbrushes?

A. 8 hours

B. 8 hours 24 minutes

C. 9 hours

D. 9 hours 46 minutes

E. 12 hours

Kudos for the right answer and explanation

1 ton / 6 hours and 1 ton/ 14 hours. How fast do these work together? The sum of their rates.

1 / 6 + 1 / 14

= 1/(2*3) + 1/(2*7)
= 7/(2*3*7) + 3/(2*3*7)
= 10 / (2*3*7)
= 5 / (3*7)
= 5 tons / 21 hours

21 hours / 5 tons

4.2 hours per 1 ton

so 8.4 hours for 2 tons.

B.
Re: Machine A can produce   [#permalink] 11 Sep 2019, 10:44
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