Bunuel wrote:

George can fill Q cans of paint in 3 minutes. If there are R cans of paint in one gallon, how many gallons can George fill in 45 minutes?

A. 30R/Q.

B. 15R/Q.

C. 30Q/R.

D. 5Q/R.

E. 15Q/R.

Another way: Choose numbers that are factors and/or multiples of 3 and 45. I set up proportion first to avoid inverting Q and R:

Q cans of paint in 3 minutes

\(\frac{Q cans}{3 mins}\) = \(\frac{X cans}{45 mins}\)

Let Q cans = 9

Let R, # of cans of paint in one gallon = 3

How many gallons do Q cans contain? 9 cans divided by 3 cans per gallon = 3 gallons.

Change the proportion units, where Q = 3

gallons:

\(\frac{3 gallons}{3 mins}\) = \(\frac{X gallons}{45 mins}\)

X = 45 gallons

Check answer choices with Q = 9, R = 3, looking for answer that yields

45A. 30R/Q = 90/9 = 10. NO

B. 15R/Q = 45/9 = 5. NO

C. 30Q/R = 270/3 = 90. NO

D. 5Q/R = 45/3 = 15. NO

E. 15Q/R = 135/3 = 45. YES

Answer E