There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses 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  Choose the correct choice from the following choices.
A) I	B) II	C) III	D) II &III	E) I &II
Name T = full pool   U fills a pool in a days ==&gt; 1 day U 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 (U+Y+Z) together fill: T(1/a + 1/b + 1/c)   d days (U+Y+Z) together fill: T   ==&gt; d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)   ==&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   II
<result>B</result>
There are three different hoses used to fill a pool: hose U, hose y, and hose z. Hose U can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses 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