Question 920224
Rates of FILLING are (+)
Rates of emptying are (-)
-----------------------
Rate of filling for pipe A:
( 1 tank ) / ( 4 hrs )
------------------------
Let {{{ -R }}} = rate of emptying for pipe C
{{{ 2R }}} = rate of filling for pipe B
( 1/2 the time means twice the rate )
------------------------------------
Add the rates with all 3 pipes open:
{{{ 1/4 + 2R - R = 1 / 2.4 }}}
Multiply both sides by {{{2.4*4 }}}
{{{ 2.4 + 19.2R - 9.6R = 4 }}}
{{{ 9.6R = 1.6 }}}
{{{ R = 1/6 }}}
---------------
{{{ -R = -1/6 }}}
In minutes:
{{{ -R = ( -1/6 )*60  }}}
{{{ -R = -10 }}}
Pipe C drains the tank in 10 min
------------------------------
check:
{{{ 1/4 + 2R - R = 1 / 2.4 }}}
{{{ 1/4 + 2*(1/6) - 1/6 = 1 / 2.4 }}} 
Multiply both sides by {{{ 12 }}}
{{{ 3 + 4 - 2 = 5 }}}
{{{ 5 = 5 }}}
OK