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Machine A can produce
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Updated on: 10 Sep 2019, 21:32
Updated on: 10 Sep 2019, 21:32
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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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Machine A can produce
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11 Sep 2019, 04:58
11 Sep 2019, 04:58
2
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
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
Answer: B
Cheers,
Brent
Re: Machine A can produce
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11 Sep 2019, 10:44
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
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.
