Bunuel wrote:

One inlet pipe can fill an empty cistern to 1/3 of its capacity in 3 hours. A second inlet pipe can fill the empty cistern to 3/4 of its capacity in 4.5 hours. If both pipes are opened simultaneously, how long, in hours, will it take to fill the cistern?

(A) 4.75

(B) 4.25

(C) 3.75

(D) 3.6

(E) 3.25

Pipe 1 rate:

\(\frac{(\frac{1}{3})}{3}=(\frac{1}{3}*\frac{1}{3})=\frac{1}{9}\)Pipe 2 rate:

\(\frac{\frac{3}{4}}{\frac{9}{2}}=(\frac{3}{4}*\frac{2}{9})=\frac{1}{6}\)Together, combined rate is

\((\frac{1}{9}+\frac{1}{6})=\frac{15}{54}=\frac{5}{18}\)W = 1 (cistern)

Rate and time are inversely proportional, and here, multiplied, they must equal 1.

Flip the rate to get the time, in hours, that it would take to fill the cistern*:

\(\frac{18}{5}= 3.6\) hours

ANSWER D

*OR

\(R*T = W\), so \(T=\frac{W}{R}\)

\(T = \frac{1}{(\frac{5}{18})}= (1* \frac{18}{5})=3.6\) hours
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"