Bunuel wrote:

x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x

B. y

C. y^2

D. x/y

E. y^2/x

Find the individual machine rate from scenario #1 (defined by \(x\)), then use that rate to find the number of widgets in scenario #2.

Scenario 1: x identical machines make x widgets in x minutes

(# of workers) * R * T = WPlug in variables*

\(x*R*x=x\)

\(Rate=\frac{x}{x^2}\)

At that rate . . .

Scenario 2: y identical machines in y minutes can make how many widgets? (= Work)

(# of workers) * R * T = W\(y*\frac{x}{x^2}*y=W\)

\(W=\frac{y*x*y}{x2}\)

\(W=\frac{y^2}{x}\)

Answer E

*In other words, manipulate the equation exactly as RT=W is manipulated with one more variable (# of machines) on LHS. Scenario #1:

\(R=\frac{W}{(No.Of.Machines*T)}\)

Scenario #2:

\(Work=(No.Of.Machines*R*T)\)