George can fill Q cans of paint in 3 minutes. If there are R cans of

Q cans in 3 minutes, so 15Q in 3*15 minutes.....
But we have to answer in terms of gallons and 1 gallon = R cans...
so in gallons 15Q =\(\frac{15Q}{R}\)..
E

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 45

A. 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

Cans / minute = Q/3

1 can of pain has 1/R gallon

Hence gallons filled / minute = Q/3R

Gallons filled in 45 mins = 45 * Q/3R = 15*Q/R

Correct Option: E

In 3 minutes total cans filled = Q
required in 45 minutes = Q/3 * 45 = 15Q

R cans comprises of 1 Gallon
so 15Q cans - 15Q/R Gallons

Correct answer is E