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Working together at their respective constant rates, robot A [#permalink]
06 Jul 2018, 16:20
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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
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Re: Working together at their respective constant rates, robot A [#permalink]
07 Jul 2018, 19:10
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Let us assume, Machine B can do x work in 1 minor, 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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Re: Working together at their respective constant rates, robot A [#permalink]
10 Jul 2018, 06:12
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ExplanationWhen 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 [ 26.04 KiB  Viewed 3215 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 [ 50.99 KiB  Viewed 3215 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 [ 28.05 KiB  Viewed 3216 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 2019, 03:47
amorphous wrote: 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 What's the reason the changing the from here, Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. to here or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min ??????
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Re: Working together at their respective constant rates, robot A [#permalink]
10 Jul 2019, 05:55
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huda wrote: amorphous wrote: 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 What's the reason the changing the from here, Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. to here or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min ?????? We want to find the time it takes to polish a certain amount of gemstone not the other way round i.e. we are not interested in finding how many gemstones can be polished in a given time.
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Re: Working together at their respective constant rates, robot A [#permalink]
13 Oct 2019, 01:22
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sandy wrote: 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 Let, Efficiency of Robot B = 5e So, Efficiency of Robot A = 3e Combined efficiency of A and B is 8e = \(\frac{88}{6}\) pounds/min Or, e = \(\frac{11}{6}\) pounds/min So, Efficiency of A = \(\frac{33}{6}\) pound/min Thus, Time taken for robot A to polish 165 gemstones is \(\frac{165*6}{33}\) = 30 minutes, Answer must be (E)N:B: Collected From GMAT
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Re: Working together at their respective constant rates, robot A [#permalink]
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Can someone explain why the combined work formula doesn't work here? I understand your methodology, but keep getting 18 using that formula. Thanks!



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Re: Working together at their respective constant rates, robot A [#permalink]
30 Apr 2020, 05:33
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dsmaier wrote: Can someone explain why the combined work formula doesn't work here? I understand your methodology, but keep getting 18 using that formula. Thanks! Question: 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 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones? You wish to use combined work formula: Let us do it: Time taken by A and B to polish 88 pounds of gems = 6 minutes Let time by B to polish 88 pounds of gems = x min So time by A to polish 88 pounds of gems = 5x/3 min => time taken by A and B to polish 88 pounds of gems = (x)(5x/3)/(x + 5x/3) = 5x/8 minutes = 6 => x = 48/5 minutes => time by A to polish 88 pounds of gems = 5x/3 = 5/3 * 48/5 = 16 minutes => time by A to polish 1 pound of gems = 16/88 minutes => time by A to polish 165 pound of gems = 16/88 * 165 = 30 minutes Obviously, it doesn't make sense to do it like this, since it is lengthy So, let us improvise: Question: 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 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones? Rate of A = 3/5 of rate of B thus: If B polishes 5x gems per minute => A will polish 3x gems per minute => Together they polish 8x gems per minute thus, in 6 minutes they will polish 8x * 6 = 48x gems thus, this 48x is actually 88 thus: 88 gems is 48x => 165 gems is 48x/88 * 165 = 90x gems A was polishing 3x gems per minute So, time = 90x/3x = 30 minutes
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Re: Working together at their respective constant rates, robot A [#permalink]
30 Apr 2020, 12:23
Thanks a ton  great seeing the comparison, much appreciated.



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Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 09:43
sandy wrote: 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 Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes.rate = output/timeSo, if 88 pounds of gemstones are polished in 6 minutes, their combined RATE = 88/6 = 44/3 gemstones per minute Let A = robot A's RATE in gemstones per minute Let B = robot B's RATE in gemstones per minute We can now write: A + B = 44/3 gemstones per minute Robot A’s rate of polishing is 3/5 that of robot BSo, we can write: A = (3/5)B If we want to solve this equation for B, we can multiply both sides by 5/3 to get: (5/3)A = B Or we can express this as: B = 5A/3We can now take our original equation: A + B = 44/3And replace B with 5A/3 to get: A + 5A/3 = 44/3Let's eliminate the fractions by multiplying both sides of the equation by 3 to get: 3A + 5A = 44 Simplify: 8A = 44 Solve: A = 44/8 = 11/2In other words, robot A's RATE = 11/2 gemstones per minute How many minutes would it take robot A alone to polish 165 pounds of gemstones?time = output/rateSo, time = 165/( 11/2) = (165)(2/11) = 330/11 = 30 minutes Answer: E Cheers, Brent
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Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 10:26
Robot A and B can polish 88 pounds of gemstones in 6 minutes. So their combines rate is\(\frac{88}{6}\) We can write this as:
\(A+B = \frac{88}{6}\) where A and B are the rates of Robot A and Robot B respectively.
Now, we are told that obot A’s rate of polishing is \(\frac{3}{5}\) that of robot B. This can be written as:
\(B = \frac{5A}{3}\)
Substituting in our rate equation, we get: \(A+\frac{5A}{3}\) = \(\frac{88}{6}\)
Solving this, we get \(A = \frac{33}{6}\)
We know, \(Work = Rate * Time\) which implies \(Time = \frac{Work}{Rate}\)
plugging the values into this formula:
\(Time = \frac{165*6}{33}\) which is 30.
Therefore the answer is (E)



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Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 19:18
Since we were given that the rate of a is 3/5 of B This can be re written as ratio inform of A:B = 3:5 From the information above we can deduce that A polish 33 gems in 6mins while B Polish 55 gems Then we can say 33gems = 6mins Then 165gems = xmins Cross multiply this we have 165*6/33 Which equal to 30 Posted from my mobile device




Re: Working together at their respective constant rates, robot A
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