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x identical machines can make x widgets in x minutes. If each machine

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Bunuel
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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   24 Apr 2017, 04:25
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x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x
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E
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maheshaero20
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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   24 Apr 2017, 11:57
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Number of Widgets is directly proportional to Number of machines and Time taken.

So we can write it as \(W ∝T*N\) ==> \(W=K*T*N\)

Where
W= Number of Widgets
T= Time Taken
N= Number of Machine
K= Equation constant (Don't Worry about this :wink:)

From the given Problem

\(x=K*x*x\)

On Solving above equation \(K=\frac{1}{x}\)

\(Wy= K*y*y\)

on substituting \(K=\frac{1}{x}\) ==> \(Wy=\frac{y^2}{x}\)


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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   24 Apr 2017, 11:31
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x machine-------x minutes---------x widgets

x machine-------1 minutes---------x /x widgets(=1 widget)

1 machine-------1 minutes---------1/x widgets (rate of x machine)

similarly
let Y machine in y minutes make A widget. then

y machine-------y minutes---------A widgets

y machine-------1 minutes---------A/y widgets

1 machine-------1 minutes---------A/y^2 widgets (rate of y machine)

As rates are equal

A/y^2 = 1/x
A =y^2/x

Ans E
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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   03 Aug 2018, 17:21
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Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x

Find the individual machine rate from scenario #1 (defined by \(x\)), then use that rate to find the number of widgets in scenario #2.

Scenario 1: x identical machines make x widgets in x minutes
(# of workers) * R * T = W
Plug in variables*
\(x*R*x=x\)
\(Rate=\frac{x}{x^2}\)

At that rate . . .
Scenario 2: y identical machines in y minutes can make how many widgets? (= Work)
(# of workers) * R * T = W
\(y*\frac{x}{x^2}*y=W\)
\(W=\frac{y*x*y}{x2}\)
\(W=\frac{y^2}{x}\)

Answer E

*In other words, manipulate the equation exactly as RT=W is manipulated with one more variable (# of machines) on LHS. Scenario #1:
\(R=\frac{W}{(No.Of.Machines*T)}\)
Scenario #2:
\(Work=(No.Of.Machines*R*T)\)
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   27 Apr 2017, 17:11
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Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x


We are given that x identical machines can make x widgets in x minutes. Thus, the rate for the x machines is x/x or 1 widget per minute. Next we can determine the rate of y machines using the following proportion in which n is the rate for y machines:

x/1 = y/n

n = y/x

Since the rate for y machines is y/x and work = rate x time, y machines can produce (y/x)(y) = y^2/x widgets in y minutes.

Answer: E
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   02 May 2017, 15:29
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x identical machines.......working x minutes......can make= x widgets

1 identical machines.......working 1 minutes......can make[less] = x/(x+x) widgets

y identical machines.......working y minutes......can make[more] = (x/(x+x))*(y*y) widgets
= y^2 /x widgets

Answer: E
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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   03 Aug 2018, 11:54
Lets say that R is the rate and W the number of widgets

\(X * R = \frac{X}{X}\)
\(R = \frac{1}{X}\)

(Replacing R)
\(Y * R = \frac{W}{Y}\)
\(Y * \frac{1}{X} = \frac{W}{Y}\)
\(\frac{Y}{X} = \frac{W}{Y}\)
\(W = \frac{Y²}{X}\)

Option E
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x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   02 May 2020, 04:54
Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x



NR.MACHINES-----------RATE-----------TIME-------------WORK
x-------------------------x/x=1----------x mins----------x widgets

Thus one single machine has rate equal to x/x=1 divided by x machines ------------> 1/x

Therefore,
NR.MACHINES-----------RATE-----------TIME-------------WORK
y-----------------------y*(1/x)=y/x-----y mins----------> rate*time=(y/x)*y=(y^2)/x
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink] New post   26 Mar 2024, 09:27
Assume x = 10 then:
10 machines in 10 minutes can make 10 widgets i.e. 1 machine makes 1 widget in 10 mins
Assume y = 20 then:
20 machines in 20 minutes can make 40 widgets since machines and time both have doubled (and all machines are identical)
If we check options, only (E) gives us 40 as an answer
We can even assume y = 5 (lower value than x), only (E) will give us the correct answer
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]
26 Mar 2024, 09:27
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