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Machine A and machine B are each used to manufacture 660 [#permalink]

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07 Aug 2010, 05:37

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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?

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?

6 6.6 60 100 110

book give a backsolving solution which I am not a big fan of...........please explain method...

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 \(rate_A*1.1=rate_B\) --> \(\frac{660}{a}*1.1=\frac{660}{a-10}\) --> \(a=110\) --> \(rate_A=\frac{job \ done}{time}=\frac{660}{a}=6\).

Thanks very much for the solution and explanation, Bunuel. One quick clarification though. In the explanation you make the jump from (660/a)*1.1 = 660/(a-10) to a = 110. Can you give a quick explanation for how you made that jump?

Thanks very much for the solution and explanation, Bunuel. One quick clarification though. In the explanation you make the jump from (660/a)*1.1 = 660/(a-10) to a = 110. Can you give a quick explanation for how you made that jump?

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?

6 6.6 60 100 110

book give a backsolving solution which I am not a big fan of...........please explain method...

Hi zisis,

Sorry you're not a fan of Kaplan's backsolving methods, but in this case it can be really helpful.

Here, a little estimation goes a long way. We know that A works 10 hours longer than B does, so if A is making 100 or 110 sprockets per hour, it would be making 1000+ sprockets--impossible! Even 60/hour is clearly too high

Given that, the correct answer has to be either A or B. So, we start where it's easiest--the whole number. If A makes 6 sprockets/hour, then A will take 110 hours to produce 660 sprockets. Meanwhile, if A makes 6 sprockets per hour and B makes 10% more, B must make 6.6 sprockets/hour. B would therefore take 100 hours to make 660 sprockets.

The question stem tells us that A should work 10 more hours than B. When we plug 6 back into the question, A does work 10 more hours than B--that confirms that A is the correct answer, with a minimum of crunchy math.
_________________

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?

6 6.6 60 100 110

book give a backsolving solution which I am not a big fan of...........please explain method...

If i form the following equation from the condition is it wrong? 660/x - 660/x+10 =10/100
_________________

Suppose rate of B is b and rate of A is a. Suppose B takes x hours to produce 660 sprockets, so 660/b = x ( b = number of sprockets produced by B in one hour ) So A takes x + 10 hours to produce 660 sprockets or 660/a = x + 10. Now it is given that B produces 10% more sprockets than A in 1 hour, hence b = 110% of a or b = 1.1a 660/b = x and 660/a = x + 10 or 660/a - 10 = x From above, 660/b = 660/a - 10 ( since both of them equals x ) Since b = 1.1a 660/1.1a = 660/a - 10 Solving above equation will give us a = 6 sprockets/hour or we can say that A produces 6 sprockets per hour. Hence answer is option A

Substituting t in rate of a... \(\frac{66}{t+10}\)gives the rate as 6.

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_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

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?

6 6.6 60 100 110

book give a backsolving solution which I am not a big fan of...........please explain method...

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 \(rate_A*1.1=rate_B\) --> \(\frac{660}{a}*1.1=\frac{660}{a-10}\) --> \(a=110\) --> \(rate_A=\frac{job \ done}{time}=\frac{660}{a}=6\).

Answer: A.

Hope it's clear.

I did a similar approach, but what I did different was I said that Rate A = 660/(x+10) and Rate B = 1.1(660/x) This is basically saying B takes x hours and A takes x+10 hours.

Why is this wrong? Because I don't get the same answer.

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?

6 6.6 60 100 110

book give a backsolving solution which I am not a big fan of...........please explain method...

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 \(rate_A*1.1=rate_B\) --> \(\frac{660}{a}*1.1=\frac{660}{a-10}\) --> \(a=110\) --> \(rate_A=\frac{job \ done}{time}=\frac{660}{a}=6\).

Answer: A.

Hope it's clear.

I did a similar approach, but what I did different was I said that Rate A = 660/(x+10) and Rate B = 1.1(660/x) This is basically saying B takes x hours and A takes x+10 hours. Why is this wrong? Because I don't get the same answer.

Thanks,

The highlighted part is not correct. Rate B = \(\frac{660}{x}\) and as Machine B makes more sprockets than Machine A, thus, by the given condition, Rate B = 1.1*Rate A.

Thus, \(\frac{660}{x} = 1.1*\frac{660}{(x+10)}\) = x+10 = 1.1x = x = 100. Thus, Per hour, Machine A would produce \(= \frac{660}{(100+10)} = \frac{660}{110)}\) = 6.
_________________

1. Let the number of sprockets produced by machine A in 1 hour be x 2. Number of sprockets produced by machine B in 1 hour is 1.1x

3. Let machine A take y hours to produce 660 sprockets. In 1 hour it produces 660/y sprockets 4. Machine B takes y-10 hours to produce 660 sprockets. In 1 hour it produces 660/y-10 sprockets

5. Equating (1) and (3) -> xy=660 6. Equating (2) and (4) -> 1.1xy-11x=660

Re: Machine A and machine B are each used to manufacture 660 [#permalink]

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24 Dec 2013, 12:46

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zisis 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

Let me chip in on this one

So we get that B manufactures the 660 sprockets in 10 hours less which indeed are 10%. Therefore total hours it takes is 100 Then A must take 10 hrs more hence 110 hours

Now, Total Work/Rate = 660/110 = 6 sprockets per hour

Machine A and machine B are each used to manufacture 660 [#permalink]

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22 Aug 2015, 13:49

Options C, D and E don't work because the numbers don't add up. It's just a matter of choosing between A and B

(E) 660/110 = 6 for A and -4 for B (X)

(D) 660/100 = 6.6 for A and -3.4 for B (X)

(C) 660/60 = 11 for A and 1 for B. But 1 is not 10% faster than A (X)

(B) 660/6.6 = 100 for and 90 for B. But 90 is not 10% faster than A - think 90*1.1=99. Almost there. (X)

Finally for option A

660/6 = 110 for A and 100 for B. 100*1.1 = 110. Correct.

The whole thing took less than a minute. As soon as you realise that C,D,E are too large it becomes a question of discarding B to get A. Similarly, at first sight 6.6 looks like a "clean number" in that it is obviously 10% greater than 6.

Machine A and machine B are each used to manufacture 660 [#permalink]

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19 Jul 2016, 05:38

zisis 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

Quick way to do this one..we will use the concept of percentages..

B produces 10% more sockets per hour..thus if per hour A produces x..B produces 1.1x

The ratio of time of the two will be inverse of the ratio of efficiencies or 1.1 : 1

The difference in these times has been given as 10 hours.. 1.1y - y = 10

y = 100 hours

A's time = 110 hours B's time = 100 hours

A's production per hour?...660/110 = 6 sprockets(A).. _________________

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