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# Machine A and Machine B can produce 1 widget in 3 hours

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Manager
Joined: 05 May 2005
Posts: 78

Kudos [?]: 59 [0], given: 0

Machine A and Machine B can produce 1 widget in 3 hours [#permalink]

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18 May 2007, 16:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2

b) 2

c) 3

d) 5

e) 6

Kudos [?]: 59 [0], given: 0

Manager
Joined: 02 May 2007
Posts: 152

Kudos [?]: 5 [0], given: 0

Re: Word Problem - machines [#permalink]

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18 May 2007, 19:26
above720 wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2

b) 2

c) 3

d) 5

e) 6

(E) it is

A = hours it takes machine A to produce 1 widget on its own
B = hours it takes machine B to produce 1 widget on its own

1/A + 1/B = 1/3
=> 3B + 3A = AB (1)

2/A + 1/B = 1/2
=> 4B + 2A = AB (2)

(1) & (2) => A = B

=> A = 6

Kudos [?]: 5 [0], given: 0

Director
Joined: 26 Feb 2006
Posts: 900

Kudos [?]: 165 [1], given: 0

Re: Word Problem - machines [#permalink]

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18 May 2007, 20:29
1
KUDOS
above720 wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2

b) 2

c) 3

d) 5

e) 6

= inverse of (1/2 - 1/3) = inverse (1/6) = 6 hours.

Kudos [?]: 165 [1], given: 0

Current Student
Joined: 22 Apr 2007
Posts: 1097

Kudos [?]: 26 [0], given: 0

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18 May 2007, 20:32
A+B = 1/3 => 3A + 3B = 1 => 6A + 6B = 2
2A+B = 1/2 => 4A + 2B = 1 => 12A + 6B = 3

Together, 6A = 1 => A = 1/6. So A takes 6 hours to produce the widget

Kudos [?]: 26 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 14831

Kudos [?]: 288 [0], given: 0

Re: Machine A and Machine B can produce 1 widget in 3 hours [#permalink]

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23 Nov 2017, 02:29
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Kudos [?]: 288 [0], given: 0

Re: Machine A and Machine B can produce 1 widget in 3 hours   [#permalink] 23 Nov 2017, 02:29
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# Machine A and Machine B can produce 1 widget in 3 hours

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