Pipe P can drain the liquid from a tank in 1/4 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?
Choose the correct choice from the following answers:
A) 9/29	B) 3/23	C) 3/8	D) 17/29	E) 3/4
Suppose Q can drain in 1 hr. So, rQ = 1/1= 
<gadget id="calculator">1/1</gadget>
<output>1</output>
1   So, rP= 1/[(1/4)rQ] = 4   Also, rP 1/ (1/4)= 
<gadget id="calculator">1/ (1/4)</gadget>
<output>4</output>
4   Also, rP= rR/(2/3) =&gt; 4 = rR/(2/3) =&gt; rR = 8/3   Let H is the time it takes to drain by running all 3 pipes simultaneously   So combined rate = rC = 1/H = 1 + 4 + 8/3 = 23/3 = 1/(3/23)   Thus running simultaneously, Pipe Q will drain 3/23 of the liquid.   Thus answer = 3/23.
<result>B</result>
Pipe P can drain the liquid from a tank in 1/4 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?