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# Machine A and machine B are each used to manufacture 660 spr

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Director
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Machine A and machine B are each used to manufacture 660 spr [#permalink]  18 May 2006, 18:34
00:00

Difficulty:

45% (medium)

Question Stats:

56% (03:21) correct 44% (02:08) wrong based on 52 sessions
Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?

A. 6
B. 6.6
C. 60
D. 100
E. 110

OPEN DISCUSSION OF THIS QUESTION IS HERE: machine-a-and-machine-b-are-each-used-to-manufacture-98696.html
[Reveal] Spoiler: OA
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Manager
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  18 May 2006, 18:52
Using POE, answers C, D and E look too big because the difference in time it takes for A and B is [u]only[/u] 10% and it takes [u]10 hrs more [/u] for A than B to make 660.

Now going by backsolving, start with A (as it's easy one without decimals :-D ).

If A makes 6/hr --> B makes 6.6/hr.
It takes A 110 hrs for 660 sprockets (ot whatever they are) and
it takes B 100 hrs for the same.

Hence A.
Manager
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  18 May 2006, 18:57
B = x hrs to produce 660
A = x + 10 hrs to produce 660

in one hr B produces 660/x
in one hr a produces 660/x + 10
660/x - 660/x+10 = 1/10(660/x+10)
solving we get x = 100
x + 10 = 110...
Thus Aproduces 660/110 =6 sprockets in an hour.

I couldnt think of a faster approach, but the above one dint take much time either.
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  18 May 2006, 22:05
Machine B: Takes x hours to produce 660 sprockets
Machine A: Takes (x+10) hours to produce 660 sprockets

Machine B: In 1 hour, B makes 660/x sprockets
Machine A: In 1 hour, A makes 660/(x+10) sprockets

Equating:

1.1(660/(x+10)) = 660/x
726/(x+10) = 660/x
726x = 660x+6600
66x = 6600
x = 100

A makes 660/(110) = 6 sprockets per hour
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  19 May 2006, 01:44
We get two equations here for number of sockets by B in 1hr

Let time taken by A for 660 sockets = x

1) B in 1 hr = 1.1 * (a in 1 hr)

ie. 1.1 * 660/x = 726/x

2) B taken 10 hrs less than A for 660 sockets

660 sockets in (x-10) hrs
Therefore 1hr = 660/x-10

Using these two,

726/x = 660/(x-10)

So, x = 110.
In 1 hr A makes 660/110 = 6 sockts
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  26 Jun 2014, 19:54
ywilfred wrote:
Machine B: Takes x hours to produce 660 sprockets
Machine A: Takes (x+10) hours to produce 660 sprockets

Machine B: In 1 hour, B makes 660/x sprockets
Machine A: In 1 hour, A makes 660/(x+10) sprockets

Equating:

1.1(660/(x+10)) = 660/x
726/(x+10) = 660/x
726x = 660x+6600
66x = 6600
x = 100

A makes 660/(110) = 6 sprockets per hour

1.726/(x+10) = 660/x
2. 726x = 660x+6600

How did you get from 1 to 2 ? where did the x+10 and x go?
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  26 Jun 2014, 20:39
Expert's post
gmatmba wrote:
Machine A and Machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machine A produce

A. 6
B. 6.6
C. 60
D. 100
E. 110

This took me a long time to calculate and figure out. Does anyone have a quick method that you can show me?

Source suggested backsolving due to time constraints.

Rate A : Rate B = 10: 11 (because machine B produces 10% more sprockets per hour. So if machine A produces 10 sprockets per hr, machine B produces 11 sprockets per hour)

Time A : Time B = 11 : 10 (Ratio of time taken by machine A and B is inverse of rate)

Now, given that it takes machine A 10 hours longer to produce 660 sprockets than machine B. So actual difference between the time taken is 10 hrs for 660 sprockets. Since difference on the ratio scale is 1, multiplier is 10.
Machine A takes 110 hrs to produce 660 sprockets and machine B takes 100 hrs to produce 600 sprockets.

So machine A makes 660/110 = 6 sprockets per hour.

For more on ratios, check: http://www.veritasprep.com/blog/2011/03 ... of-ratios/
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Re: Machine A and machine B are each used to manufacture 660 spr [#permalink]  27 Jun 2014, 01:47
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Expert's post
gmatmba wrote:
Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?

A. 6
B. 6.6
C. 60
D. 100
E. 110

OPEN DISCUSSION OF THIS QUESTION IS HERE: machine-a-and-machine-b-are-each-used-to-manufacture-98696.html

Let time needed for machine A to produce 660 sprockets be a hours, then the rate of machine A would be rate_A=\frac{job \ done}{time}=\frac{660}{a} sprockets per hour;

As "it takes machine A 10 hours longer to produce 660 sprockets than machine B" then time needed for machine B to produce 660 sprockets be a-10 hours and the rate of machine B would be rate_B=\frac{job \ done}{time}=\frac{660}{a-10} sprockets per hour;

As "machine B produces 10 percent more sprockets per hour than machine A" then rate_A*1.1=rate_B --> \frac{660}{a}*1.1=\frac{660}{a-10} --> a=110 --> rate_A=\frac{job \ done}{time}=\frac{660}{a}=6.

OPEN DISCUSSION OF THIS QUESTION IS HERE: machine-a-and-machine-b-are-each-used-to-manufacture-98696.html
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Re: Machine A and machine B are each used to manufacture 660 spr   [#permalink] 27 Jun 2014, 01:47
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