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If 30 machines, each working at the same constant rate, together can p

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If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 24 Jul 2017, 10:09
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If 30 machines, each working at the same constant rate, together can produce \(\frac{n}{2}\) units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?


A. 30
B. 40
C. 45
D. 50
E. 60

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Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 24 Jul 2017, 10:24
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niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce \(\frac{n}{2}\) units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?


A. 30
B. 40
C. 45
D. 50
E. 60


\(30\) machines - \(n\) units - \(30\) days.

\(x\) machines - \(2n\) units - \(30\) days => \(x = 60\).

\(y\) machines - \(2n\) units - \(45\) days = \(\frac{30*60}{45} = y = 40\). Ans - B.
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Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 24 Jul 2017, 10:25
1
Let, Rate of 1 machine = R
Rate of 30 machines = 30R

Work done by 30 machines together for 15 days = 15 * 30R = 450R

Given 30 machines together can produce n/2 units of an item in 15 days

==> 450R = n/2

==> n = 900R

Let number of machines needed to produce 2n units of the item in 45 days = X

==> R * X * 45 = 2n

==> R * X * 45 = 2 * 900R

==> X * 45 = 2 * 900

==> X = 2 * 20 = 40

Answer is B
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If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 24 Jul 2017, 10:43
niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce \(\frac{n}{2}\) units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?

A. 30
B. 40
C. 45
D. 50
E. 60


Let n = 180, n/2 = 90, 2n = 360 (180 is divisible by every number in the prompt)

# of machines * R * T = W

1. 30 machines make 90 units (\(\frac{n}{2})\) in 15 days

30 * R * 15 = 90

Rate of individual machine = \(\frac{90}{450}\) ===> \(\frac{1}{5}\)

2. How many machines needed to make 360 units (2n) in 45 days?

(# of machines) * \(\frac{1}{5}\) * 45 = 360

# of machines = \(\frac{360}{9}\) = 40

Answer B
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Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 24 Jul 2017, 10:51
Step 1: Find unit/day of 1 machine.
= n/900 (unit/day)
Step 2: Set Equation
x machines * n/900 (unit/day) * 45 (no. of days) = 2n (targeted units)
x = 40 machines
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Re: If 30 machines, each working at the same constant rate, together can p  [#permalink]

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New post 26 Jul 2017, 16:36
niteshwaghray wrote:
If 30 machines, each working at the same constant rate, together can produce \(\frac{n}{2}\) units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?


A. 30
B. 40
C. 45
D. 50
E. 60


We are given that the rate of 30 machines is (n/2)/15 = n/30.

We can create the following proportion to determine the number of machines needed to work at a rate of 2n/45, letting x = the number of machines needed:

30/(n/30) = x/(2n/45)

900/n = 45x/2n

1800n = 45xn

40 = x

Answer: B

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Re: If 30 machines, each working at the same constant rate, together can p   [#permalink] 26 Jul 2017, 16:36
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