Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?
(1) Working alone, Machine B takes 5 hours to produce 50 widgets.
(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.
[spoiler]OA=D[/spoiler]
Source: Magoosh
Working together, Machine A and Machine B can produce
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Say working alone, Machine A can produce 200 widgets in a hours and Machine B can produce 200 widgets in b hours. Thus, we haveVJesus12 wrote:Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?
(1) Working alone, Machine B takes 5 hours to produce 50 widgets.
(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.
[spoiler]OA=D[/spoiler]
Source: Magoosh
1/a + 1/b = 1/4
We have to get the value of a.
Let's take each statement one by one.
(1) Working alone, Machine B takes 5 hours to produce 50 widgets.
=> Working alone, Machine B takes 5*4 = 20 hours to produce 50*4 = 200 widgets.
=> b = 20
Thus, from 1/a + 1/b = 1/4, we have
1/a + 1/20 = 1/4
1/a = 1/4 - 1/20
1/a = 4/20
a = 5. Sufficient.
(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.
=> b = 4a
Thus, from 1/a + 1/b = 1/4, we have
1/a + 1/4a = 1/4
5/4a = 1/4
a = 5. Sufficient.
The correct answer: D
Hope this helps!
-Jay
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