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Working together at their respective constant rates, robot A

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Working together at their respective constant rates, robot A [#permalink] New post 06 Jul 2018, 16:20
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Question Stats:

54% (01:47) correct 45% (02:21) wrong based on 11 sessions
Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is \(\frac{3}{5}\)that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?

(A) 15.75
(B) 18
(C) 18.75
(D) 27.5
(E) 30
[Reveal] Spoiler: OA

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Re: Working together at their respective constant rates, robot A [#permalink] New post 07 Jul 2018, 19:10
Let us assume,

Machine B can do x work in 1 min
or, Machine B can do \(6x\) work in \(6 min\)

It follows that Machine A is only 3/5 efficient as machine A hence,
Machine A can do \(\frac{18}{5} x work in 6 min.\)

From question,

\(\frac{18}{5} x + 6x = 88\)
because working together the two machines can polish \(88 pounds\) of gemstone in \(6 min.\)

solving for x we get \(x = \frac{440}{48}\)
This is the pound of gemstone machine B can polish in 1 min.
The amount of gemstone that machine A can polish in 1 min is \(\frac{440}{48} * \frac{3}{5}\)
Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min.
or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min
or, Machine A can polish 165 pound of gemstone in \(\frac{240}{1320} * 165\) min = 30 min
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [1] , given: 375

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Re: Working together at their respective constant rates, robot A [#permalink] New post 10 Jul 2018, 06:12
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Explanation

When rate problems involve multiple situations, it can help to set up an initial “skeleton” W= RT chart for the solution. That way, you can determine what data is needed and fill in that data as you find it. Since the question asks how long robot A will take alone, the chart will look like this:

Attachment:
image1.jpg
image1.jpg [ 26.04 KiB | Viewed 327 times ]


Work is known and the question asks for time, so robot A’s rate is needed. Call the rates a and b. Now set up another chart representing what you know about the two robots working together.

Attachment:
image1.jpg
image1.jpg [ 50.99 KiB | Viewed 327 times ]


Now, 6(a + b) = 88 and, from the question stem, robot A’s rate is \(\frac{3}{5}\) of B’s rate. This can be written as \(a = \frac{3}{5}b\). To solve for a, substitute for b:

\(a = \frac{3}{5} b\)
\(\frac{5}{3}a = b\)

\(6(a+ \frac{5}{3}a) = 88\)

\(6 \frac{8}{3} a = 88\)
\(a = \frac{11}{2}\)

So A’s rate is pounds per minute. Now just plug into the original chart:

Attachment:
image1.jpg
image1.jpg [ 28.05 KiB | Viewed 327 times ]


The time robot A takes to polish 165 pounds of gems is \(165/\frac{11}{2} =\frac{330}{165} = 30\) minutes.
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Re: Working together at their respective constant rates, robot A   [#permalink] 10 Jul 2018, 06:12
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