There are three different hoses used to fill a pool: hose U, hose V, and hose W. Hose x 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 Choices:
A) I	B) III	C) I and II only	D) II & III	E) II
Name T = full pool   U fills a pool in a days ==&gt; 1 day U fills: T/a   V fills a pool in b days ==&gt; 1 day V fills: T/b   W fills a pool in c days ==&gt; 1 day W fills: T/c   1 day (U+V+W) together fill: T(1/a + 1/b + 1/c)   d days (U+V+W) 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>E</result>
There are three different hoses used to fill a pool: hose U, hose V, and hose W. Hose x 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