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Re: Machine A, working alone at its constant rate, produces x [#permalink]
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sandy wrote:
Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?



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7.2


Practice Questions
Question: 16
Page: 85



Let,
Ra = Time taken by MAchine A

Rb = Time taken by machine B

Working together, time taken is given by: \(\frac{{Ra * Rb}}{(Ra + Rb)}= \frac{{12 * 18}}{(12 + 18)}= \frac{{12 * 18}}{30} = 7.2\)


***Total Rate when working together = \(\frac{{Ra + Rb}}{(Ra * Rb)}\)
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Re: Machine A, working alone at its constant rate, produces x [#permalink]
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Finally, a work problem that I understand!

From the question, we can set up two W R T equations and solve for R, where Work is the X pounds produced
Machine A: X = 12r
Machine A's rate is x/12 (we just solve for r above by dividing both sides by 12)

Machine B: X = 18r
Machine B's rate is x/18 (solve for r by dividing both sides by 18.

Then, to get the combined rate, we just add the rates together:
x/12 + x/18
LCD is 36 (12*3 and 18*2)
3x/36 + 2x/36 = 5x/36 or (5/36)x

Now, we can take the rate and plug it into our equation to solve for T
X = (5/36)x*T
divide both sides by (5/36)x
36/5 = T = 7.2
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Re: Machine A, working alone at its constant rate, produces x [#permalink]
let the x = 36w
so A's rate = 36w/12 = 3w
B's rate = 36w/18 = 2w
simultaneous work = A +B rate = 5w
time taken will be = 36w/5w = 7.2
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Re: Machine A, working alone at its constant rate, produces x [#permalink]
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