There are three different pipes used to fill a pool: pipe x, pipe y, and pipe z. Pipe x can fill the pool in a days, pipe y in b days, and pipe z in c days, where a > b > c. When all three pipes are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Select
A) II B) I C) III D) I&II E) II &III
Name T = full pool   X fills a pool in a days ==&gt; 1 day X fills: T/a   Y fills a pool in b days ==&gt; 1 day Y fills: T/b   Z fills a pool in c days ==&gt; 1 day Z fills: T/c   1 day (X+Y+Z) together fill: T(1/a + 1/b + 1/c)   d days (X+Y+Z) together fill: T   ==&gt; d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)   II   ==&gt;d = abc/(ab+bc+ca)   d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
<result>A</result>
There are three different pipes used to fill a pool: pipe x, pipe y, and pipe z. Pipe x can fill the pool in a days, pipe y in b days, and pipe z in c days, where a > b > c. When all three pipes are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3