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Working together at their respective constant rates, Machine A and Mac [#permalink]
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07 Mar 2016, 09:12
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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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07 Mar 2016, 10:45
Bunuel wrote: Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8hour shift, what percent of the 1,200 unit total would it produce?
A. 25 B. 33 C. 50 D. 67 E. 75 both machines together take 8 hours for 1200 units = 150 per hour machine B takes 50% extra for same no of units , it therefore does 1200 units in 12 hours = 100 per hour machine A can produce 150100 = 50 per hour in 8 hours machine A can produce 50*8=400 units difference = (800)A  (400)B = 50%



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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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09 Mar 2016, 05:31
It says A+B produces 1200 units in 8 hours, which means in 1 hour A&B together will produce 1200/8=150 units.
Then the question says that B takes 50% more time to produce same number of units which means for B to produce 1200 units it will take( 8+50% of 8) hours= 12 hours, so B would produce 1200/12= 100 units in 1 hour.
Which would mean A would produce ((A+B)B)i.e. (150100) units/hour, units in 1 hour= 50 units.
Finally the question asks if A were to work on its own for an 8hour shift, what percent of the 1,200 unit total would it produce, so in 8 hours A would produce 50*8= 400 units which is 33% of 1200.
Hence i got 33%.



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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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09 Mar 2016, 05:38
CounterSniper wrote: Bunuel wrote: Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8hour shift, what percent of the 1,200 unit total would it produce?
A. 25 B. 33 C. 50 D. 67 E. 75 both machines together take 8 hours for 1200 units = 150 per hour machine B takes 50% extra for same no of units , it therefore does 1200 units in 12 hours = 100 per hour machine A can produce 150100 = 50 per hour in 8 hours machine A can produce 50*8=400 units difference = (800)A  (400)B = 50% Hi CounterSniper, You have done everything correctly apart from choosing the right answer.. so A does 400 in 8 hours, 400 is 400/1200 *100%=33.33%..
Its very important to choose the answer very carefully and see what is asked..
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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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21 Jul 2016, 07:25
total rate x total time = work done by A & B together. Rate(AB tog.) = (1200/8) unit/hr = 150 unit/hr
while b does the work in = 8 hrs + 50/100(8) =12 hrs and B does the same work thus rate of B= 1200/12 hrs =100 unit/hr
rate(AB) = rate A + rate B => 150 = rate A + 100 => rate A =50 unit/hr
Now rateA * time taken by A = work done ( time is 8 hr shift) => 50 * 8 =work done = 400 units by A alone
Now, x% of 1200 = 400 thus x = 33%



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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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21 Jul 2016, 09:08
Bunuel wrote: Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8hour shift, what percent of the 1,200 unit total would it produce?
A. 25 B. 33 C. 50 D. 67 E. 75 1/A+1/B= 1/T 1/A +1/12= 1/8 (50% more of 8 is 12) 1/A= 1/24 Machine A can produce 1200 units in 24 hrs, so it can produce 1200*8/24= 400 units is 8 hrs. 400 is 33.33% of 1200. B is the answer
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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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21 Oct 2017, 11:21
Both can do 1200 in 8 hours... Then 1200/8 = 150
A and B can do 150 in 1 hour
B can do the same amount in 50% more time... If A and B can do 150 in 1 hour, 1(0.5) = 0.5 = 50% more time
Add that to 1 hour = 1.5 hours to do 150 for machine B
150/1.5 = 100... Machine B can do 100 in an hour.
150  100 = 50 for machine A in an hour.
The total job took 8 hours to complete with A and B working Together so... A can do 50 in an hour: 50(8) = 400 was done by machine A. B can do 100 in an hour: 100(8) = 800 was done by machine B. 800+400 = 1,200.
The question asks for what percent of the work was done by machine A so... 400/1200 = 0.333 = 33.33% B



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Working together at their respective constant rates, Machine A and Mac [#permalink]
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21 Oct 2017, 14:33
Bunuel wrote: Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8hour shift, what percent of the 1,200 unit total would it produce?
A. 25 B. 33 C. 50 D. 67 E. 75 Combined rate is \(\frac{W}{hr} = \frac{units}{hr}\) \(\frac{1}{A} + \frac{1}{B} = \frac{1200u}{8hrs} = \frac{150u}{1hr}\) Alone, B takes 50 percent more time to finish 1200 \(u\): (8 hrs) * 1.5 = 12 hrs B's rate = \(\frac{1200u}{12hrs} = \frac{100u}{1hr}\) A's rate: (Combined rate)  (B's rate) \((\frac{150}{1hr} \frac{100}{1hr})=\frac{50u}{1hr}\) A works for 8 hours. \(r*t=W\)A completes \(\frac{50u}{1hr}\) * 8hrs = 400 units What percent is 400 of 1200? \(\frac{400}{1200}=\frac{1}{3}=.33*100 =\) 33 percent Answer B
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Re: Working together at their respective constant rates, Machine A and Mac [#permalink]
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21 Oct 2017, 19:44
 Machine A and Machine B can produce 1,200 units in 8 hours => in 1 hour they can produce: 1200/8 = 150 units.  Machine B would complete that same output in 50% more time => to produce 150 units, it takes B: 1,5 hours. => In 1 hour B can produce: 150: 1,5 = 100 units. => In 1 hour A can produce: 150  100 = 50 units. => If Machine A were to work on its own for an 8hour shift, it can produce: 50*8 = 400 units = 33,33% of total 1200 units Hence the answer is B.  Kindly press Kudos if the explanation is clear. Thank you



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Working together at their respective constant rates, Machine A and Mac [#permalink]
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09 Nov 2017, 11:24
There is no need to compute the combined work rate. Not sure why everyone is doing that. There is no advantage by finding out how many units both A and B produce in 1 hour. We are already given that A & B produce 1200 units in 8 hours. B produces 1200 units in 8+(0.5 *8) = 12 hours or 100 units per hour. Hence, we can say that among the 1200 units in 8 hours, B produced 800 units. Remaining 400 units were produced by A. Hence the ratio is 400/1200 = 1/3 or 33 %
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Working together at their respective constant rates, Machine A and Mac
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