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A machine that produces stroopwafels operates for four hours. During t

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A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 15 May 2015, 01:29
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A machine that produces stroopwafels operates for four hours. During the first hour the machine works at a constant rate. During the next two hours, it works at double that rate, and during the last hour it works at double its previous rate. If the machine produces X stroopwafels during the three first hours, then during the four hours the machine produces how many stroopwafels?

A. 4/5X
B. 9/5X
C. 2X
D. 9/4X
E. 7/3X

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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 15 May 2015, 02:48
What do you mean by - three first hours ?
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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 15 May 2015, 03:31
2
Given
We are given the rates of the machines for 4 hours of its operations. We are told that if the machine produces \(x\) stroopwafels in the first 3 hours of its operation, what would be the total stroopwafels produced by machine in 4 hours.

Approach
We know that Work = Rate * Time. Since we are given a relation between the rates of the machine during each hour and we know the time taken we can calculate the amount of work done.

Working Out
Let's assume the rate of machine in the 1st hour to be r stroopwafels/hour i.e. it can produce r stroopwafels in the first hour. So the rate of machine in the 2nd and 3rd hour would be 2r and the in the 4th hour would be 4r. Let's now find out the amount of stroopwafels produced during each hour

Stroopwafels produced in 1st hour = r * 1 = r

Stroopwafels produced in the 2nd hour = 2r * 1 = 2r

Stroopwafels produced in the 3rd hour = 2r * 1 = 2r

Stroopwafels produced in the 4th hour = 4r * 1 = 4r

We are given that amount of stroopwafels produced first three hours is \(x\) i.e. (r +2r +2r) = 5r = \(x\). We are asked to find the number of stroopwafels produced in four hours by the machine in terms of \(x\) .

Since 5r = \(x\), the amount of stroopwafels produced during the 4th hour = 4r = \(\frac{4x}{5}\).

Therefore total stroopwafels produced in 4 hours by the machine is \(x + \frac{4x}{5} = \frac{9x}{5}\)

Hope its clear :)

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Harsh
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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 15 May 2015, 06:30
reto wrote:
A machine that produces stroopwafels operates for four hours. During the first hour the machine works at a constant rate. During the next two hours, it works at double that rate, and during the last hour it works at double its previous rate. If the machine produces X stroopwafels during the three first hours, then during the four hours the machine produces how many stroopwafels?

A. 4/5X
B. 9/5X
C. 2X
D. 9/4X
E. 7/3X



Sigh. I picked A because I was solving for the ratio of the 4th hour to the first 3 hours. Reading is very important.
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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 15 May 2015, 14:57
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Hi reto,

This question, while wordy, is perfect for TESTing VALUES..

We're given a series of production rates for a machine. Let's TEST VALUES:

To start, let's say the machine creates 2 items/hour in the first hour.
During the next 2 hours, the rate doubles, so we have 4 items/hour for 2 hours.
Finally, during the last hour, the rate doubles again, so we have 8 items/hour for the last hour.

X is the total number of items during the first 3 hours, so X = 2+4+4 = 10 items

We're asked for the number of items made during all 4 hours (relative to the value of X); the total number of items in all 4 hours is 2+4+4+8 = 18 items.

Since the answers are all DIFFERENT fractions, each will give us a different answer when X=10....we're looking for whichever one equals 18.....

Answer B: (9/5)(10) = 18 This is a MATCH

Final Answer:

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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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New post 23 Dec 2016, 13:17
reto wrote:
A machine that produces stroopwafels operates for four hours. During the first hour the machine works at a constant rate. During the next two hours, it works at double that rate, and during the last hour it works at double its previous rate. If the machine produces X stroopwafels during the three first hours, then during the four hours the machine produces how many stroopwafels?

A. 4/5X
B. 9/5X
C. 2X
D. 9/4X
E. 7/3X


let r=initial rate
5r+4r=9r=total units produced in 4 hours
5r=x
r=x/5
substituting,
9*x/5=9x/5=total units produced in 4 hours
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Re: A machine that produces stroopwafels operates for four hours. During t  [#permalink]

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