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Machines X and Y produce bottles at their respective constant rates. [#permalink]

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29 Aug 2010, 20:43

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Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

Re: Machines X and Y produce bottles at their respective constant rates. [#permalink]

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31 Aug 2010, 08:26

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

formula is work = rate x time

for machine (X) k= r X 6 for machine (Y) k= r X 2 now take a value for k ( for ease which is a multiple of both mac X & y) take k=12 so rate of machine (x) is 2 so rate of machine (y) is 6

now work is 12k = 12x12 = 144 two machines working siman so rate = 6+2 =8 work = rate X time 144 = 8 X time so time = 18 so answer D

Re: Machines X and Y produce bottles at their respective constant rates. [#permalink]

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20 Feb 2015, 10:34

Safiya wrote:

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

This is an example of a Work Formula question with a minor 'twist.' The "math" in these questions can be done in a few different ways, but since we have 2 machines working on a task together, without any major "twists" (e.g. one of them stops working at a certain point), we can use the Work Formula:

Work = (A)(B)/(A+B) where A and B are the respective rates of the two machines to do the same task individually.

We're told: 1) Machine X can produce K bottles in 6 hours. 2) Machine Y can produce K bottles in 2 hours.

(6)(2)/(6+2) = 12/8 = 1.5 hours to produce K bottles when working together.

The minor 'twist' is that the question asks how long it takes to produce 12K bottles (not K bottles), so we have to multiply this result by 12...

Re: Machines X and Y produce bottles at their respective constant rates. [#permalink]

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Re: Machines X and Y produce bottles at their respective constant rates. [#permalink]

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30 Jan 2017, 04:17

1) First of all we need to find the rates of each machine: \(r*t=w. X: r*6=k, r=\frac{k}{6}; Y: r*2=k, r=\frac{k}{2}\) 2) Now we need to combine the two rates: \(\frac{k}{6}+\frac{k}{2}=\frac{4k}{6}=\frac{2k}{3}\) 3) \(\frac{2k}{3}*R=12k, R=12k/\frac{2k}{3}, R=\frac{12k*3}{2k}=18\)

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

(A) 8 (B) 12 (C) 15 (D) 18 (E) 24

We are given that machine X produces k bottles in 6 hours and thus has a rate of k/6. We are also given that machine y produces k bottles in 2 hours and thus has a rate of k/2. We need to determine how many hours it takes machines X and Y to produce 12k bottles when working together. If we let t = the time it takes the two machines working together, we can create the following equation and determine t:

(k/6)t + (k/2)t = 12k

Multiplying the entire equation by 6, we have:

kt + 3kt = 72k

Dividing the entire equation by k, we have:

t + 3t = 72

4t = 72

t = 18 hours

Answer: D
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