Pipe P can drain the liquid from a tank in 4/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?  Answers:
A) 9/29 B) 8/23 C) 3/4 D) 17/29 E) 3/8
Suppose Q can drain in 1 hr. So, rQ = 1/1= 
<gadget id="calculator">1/1</gadget>
<output>1</output>
1   So, rP= 1/[(4/4)rQ] = 4/4= 
<gadget id="calculator">4/4</gadget>
<output>1</output>
1   Also, rP= rR/(2/3) =&gt; 1 = rR/(2/3) =&gt; rR = 2/3   Let H is the time it takes to drain by running all 3 pipes simultaneously   So combined rate = rC = 1/H = 1 + 1 + 2/3 = 8/3 = 1/(3/8)   Thus running simultaneously, Pipe Q will drain 3/8 of the liquid.   Thus answer = 3/8.
<result>E</result>
Pipe P can drain the liquid from a tank in 4/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?