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

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Math Expert
Joined: 02 Sep 2009
Posts: 49276
x identical machines can make x widgets in x minutes. If each machine  [#permalink]

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24 Apr 2017, 04:25
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63% (01:11) correct 37% (01:39) wrong based on 167 sessions

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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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Joined: 05 Mar 2015
Posts: 984
x identical machines can make x widgets in x minutes. If each machine  [#permalink]

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24 Apr 2017, 11:31
1
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]

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24 Apr 2017, 11:57
1
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 $$K=\frac{1}{x}$$ ==> $$Wy=\frac{y^2}{x}$$

Kudos +1
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Re: x identical machines can make x widgets in x minutes. If each machine  [#permalink]

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27 Apr 2017, 17:11
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1
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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]

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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
Intern
Joined: 23 Aug 2017
Posts: 25
x identical machines can make x widgets in x minutes. If each machine  [#permalink]

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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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Joined: 22 May 2016
Posts: 1978
x identical machines can make x widgets in x minutes. If each machine  [#permalink]

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03 Aug 2018, 17:21
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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x identical machines can make x widgets in x minutes. If each machine &nbs [#permalink] 03 Aug 2018, 17:21
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