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One machine, working at a constant rate, can fill a certain production

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One machine, working at a constant rate, can fill a certain production [#permalink]

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One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
[Reveal] Spoiler: OA

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Re: One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 04 Apr 2018, 23:58
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours
Work done in 8 hrs = 1
Work done in 1 hr = 1/8

Work done by 4 machines in 1 hr = 1/2
So full work will be done in 2 hrs.

Ans is option A

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Re: One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 05 Apr 2018, 01:55
R * T = W
1 machine 1/8
4 machines 4 * 1/8 = 1/2

Work(4 machines)=1/2*t=1
t=2

(A)
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One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 05 Apr 2018, 08:21
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours


If the total production order is 32 units,
one machine(time taken: 8 hours) will do the work at 4 units/hour.

4 such machines, working at the same constant rate, will do 16 units of work in an hour.

Therefore, the times taken by the four machines to fill the order is \(\frac{32}{16} = 2\)hours(Option A)
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One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 07 Apr 2018, 16:45
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours


8 hrs for 1 unit of work(by single machine.)
1 hr for 1/8 unit of work(by single machine.)

1 machine 1/8 of work.
4 machines 4*(1/8) work=1/2 work. Hence, (A) it will take 2 hrs for 4 identical machines.
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One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 07 Apr 2018, 21:47
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours

Modify \(RT = W\). Add one variable to LHS.
Manipulate it the same way.

Let \(N\) = Number of machines or workers
Modified formula: \(N*R*T = W\)
(N*R*T=W table makes this way easy to see)

Scenario 1:
One machine can finish the work in 8 hours
\(W = 1\) job
\(T = 8\) hours

Standard formula to find individual rate:\(RT=W\)
Rate of one machine, \(R=\frac{W}{T}\)
\(R = \frac{1}{8}\)

Scenario 2:
At that rate, how long will it take 4 machines to finish W?
\(N = 4, R = \frac{1}{8}, W = 1\)
\(N*R*T=W\). So

\(T = \frac{W}{(N*R)}\)

\(T =\frac{1}{(4*\frac{1}{8})}\)

\(T=\frac{1}{(\frac{4}{8})}=\frac{1}{(\frac{1}{2})}=1*\frac{2}{1}=2\) hours

Answer A
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Re: One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 08 Apr 2018, 01:25
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours


Straight 2 .....

Use unitary method to solve such questions:

1 machine ----------- 8 hours
4 machines ------------ 8/4 = 2 hours !

Ans = A
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Re: One machine, working at a constant rate, can fill a certain production [#permalink]

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New post 10 Apr 2018, 11:05
Bunuel wrote:
One machine, working at a constant rate, can fill a certain production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours



Since the rate of one machine is 1/8, the rate of four machines is 4 x 1/8 = 1/2.

So it would take four machines 1/(1/2) = 2 hours to complete the order.

Answer: A
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Re: One machine, working at a constant rate, can fill a certain production   [#permalink] 10 Apr 2018, 11:05
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