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A machine can produce p fan blades in an hour. How many fan blades can this machine produce in q minutes?

A. pq

B. 60p/q

C. 60pq

D. p/(60q)

E. pq/60

Per minute: P/60
in q minutes: PQ/60 option E
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Blades produced in 1 hr = P
Blades produced in 1 mint = P/60
Blades produced in Q mints = (P/60)*Q or PQ/60 ....ANSWER = E
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Bunuel
A machine can produce p fan blades in an hour. How many fan blades can this machine produce in q minutes?

A. pq

B. 60p/q

C. 60pq

D. p/(60q)

E. pq/60

The machine can produce p x q/60 = pq/60 fan blades in q minutes.

Alternate Solution:

The machine can produce p/60 fan blades in one minute. Let’s let x = the number of fan blades the machine can produce in q minutes. Thus, we can set up the proportion:

(p/60)/1 = x/q

pq/60 = x

Answer: E
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The correct answer is **B. 60p/q**.

Let's break down the problem step by step:

1. The machine e.g. a ceiling fan can produce *p* fan blades in an hour.
2. There are 60 minutes in an hour.

Now, we want to find out how many fan blades the machine like a ceiling fan can produce in *q* minutes.

To do this, we need to establish a ratio of time. Since the machine can produce *p* fan blades in 60 minutes (1 hour), it will produce *x* fan blades in *q* minutes.

We can set up a proportion:

*p fan blades / 60 minutes = x fan blades / q minutes*

Solving for *x* (the number of fan blades in *q* minutes):

*x = (p * q) / 60*

So, the machine can produce *pq/60* ceiling fan blades in *q* minutes. However, since we are looking for the number of fan blades per minute, we can simplify the expression by dividing both the numerator and the denominator by 60:

*x = (pq) / (60 * 60) = (pq) / 3600*

Recall that there are 60 minutes in an hour, so the correct answer is *pq/3600*. However, none of the options provided exactly match this expression. To find the most appropriate choice, we can simplify *pq/3600* further:

*pq/3600 = (pq) / (6 * 600) = (pq) / (2 * 3 * 600) = (pq) / (2 * 1800) = (pq) / 3600*

So, among the given choices, the most accurate answer is **B. 60p/q**, which is the same as *pq/3600* but expressed in a more simplified form.
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