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# Working together at their respective constant rates, Machine A and Mac

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Math Expert
Joined: 02 Sep 2009
Posts: 47035
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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35% (medium)

Question Stats:

72% (01:39) correct 28% (01:45) wrong based on 260 sessions

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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 8-hour shift, what percent of the 1,200 unit total would it produce?

A. 25
B. 33
C. 50
D. 67
E. 75

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Concentration: Strategy, General Management
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 8-hour 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 150-100 = 50 per hour
in 8 hours machine A can produce 50*8=400 units

difference = (800)A - (400)B = 50%
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Joined: 09 Jan 2016
Posts: 2
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. (150-100) units/hour, units in 1 hour= 50 units.

Finally the question asks if A were to work on its own for an 8-hour 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%.
Math Expert
Joined: 02 Aug 2009
Posts: 6218
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 8-hour 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 150-100 = 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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Joined: 05 Jan 2016
Posts: 11
Location: United States
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 8-hour 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.

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Joined: 11 Oct 2017
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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
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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 8-hour 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

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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
1
- 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 8-hour shift, it can produce: 50*8 = 400 units = 33,33% of total 1200 units

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Joined: 22 Nov 2016
Posts: 236
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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
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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   [#permalink] 09 Nov 2017, 11:24
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