<PRE><B>Question 573666</B>
A tank can be filled using hose A alone in 3 hours, using hoses A and B together in 72 minutes, and using hoses A, B and C together in 40 minutes.
 How many minutes will it take to fill the same tank using only hose C?
:
Find how long for B to fill it alone
Let a full tank = 1
Convert 3 hrs to 180 min
:
{{{72/180}}} + {{{72/B}}} = 1
multiply by 180B, results
72B + 180(72) = 180B
12960 = 180B - 72B
12960 = 108B
B = {{{12960/108}}}
B = 120 minutes, B alone
:
Find C
{{{40/180}}} + {{{40/120}}} + {{{40/C}}} = 1
multiply by 360C, results:
2C(40) + 3C(40) + 360(40) = 360C
80C + 120C + 14400 = 360C
14400 = 360C - 200C 
14400 = 160C
C = {{{14400/160}}}
C = 90 minutes for C alone
:
:
Check that using decimals
{{{40/180}}} + {{{40/120}}} + {{{40/90}}} = 
.22 + .33 + .44 = .99 ~ 1 a full tank</PRE>