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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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04 Apr 2018, 23:52
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Question Stats:

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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

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Posts: 182
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Re: One machine, working at a constant rate, can fill a certain production  [#permalink]

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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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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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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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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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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

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

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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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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.

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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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