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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