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# Machine X, working alone at its constant rate, produces 1000 parts in

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Math Expert
Joined: 02 Sep 2009
Posts: 58420
Machine X, working alone at its constant rate, produces 1000 parts in  [#permalink]

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26 Sep 2018, 05:16
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:34) correct 6% (01:44) wrong based on 45 sessions

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Machine X, working alone at its constant rate, produces 1000 parts in 3 hours. Machine Y, working alone at its constant rate, produces 1000 numbers of same parts in 2 hours. Machine Z, working alone at its constant rate, produces 1000 numbers of same parts in 6 hours. How many hours will it take machines X, Y, and Z, working together at their respective constant rates, to produce 3,000 numbers of same parts?

(A) 1.50
(B) 1.75
(C) 2.50
(D) 2.75
(E) 3.00

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Re: Machine X, working alone at its constant rate, produces 1000 parts in  [#permalink]

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28 Sep 2018, 06:15
lets determine the actual rate per machine
R = W/T = 1/T x W
W = 1000 units in each case
A: 1/3 of 1000 per hour (i'm explicitly not writing 333,33 cause it makes it more confusing than needed)
B: 1/2 of 1000 per hour
C: 1/6 of 1000 per hour
A+B+C sum of their rates
bring everything to the same denominator:
->x/6
A: 2/6
B: 3/6
C: 1/6

sum: 6/6 of 1000 units per hour (so 1x 1000 units per hour)
we could have also used the values instead of fractions in which case we would have had 333,33 + 500 + 166,6667 = 1000

question is asking how long it takes to do 3000 units
at 1000 units/hour ==> 3 hours

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Re: Machine X, working alone at its constant rate, produces 1000 parts in  [#permalink]

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29 Sep 2018, 18:03
Bunuel wrote:
Machine X, working alone at its constant rate, produces 1000 parts in 3 hours. Machine Y, working alone at its constant rate, produces 1000 numbers of same parts in 2 hours. Machine Z, working alone at its constant rate, produces 1000 numbers of same parts in 6 hours. How many hours will it take machines X, Y, and Z, working together at their respective constant rates, to produce 3,000 numbers of same parts?

(A) 1.50
(B) 1.75
(C) 2.50
(D) 2.75
(E) 3.00

The combined rate of X, Y, and X is:

1000/3 + 1000/2 + 1000/6 = 2000/6 + 3000/6 + 1000/6 = 6000/6 = 1000 parts per hour

So it will take 3000/1000 = 3 hours to produce 3,000 numbers of the same parts.

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Re: Machine X, working alone at its constant rate, produces 1000 parts in   [#permalink] 29 Sep 2018, 18:03
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