Question 877095
(1)
In words:
( rate of filling container ) x ( time to fill container )
minus
( rate of leaking from container ) x ( time to fill container )
equals
( the size of the container in gallons )
------------------------------------
(2)
Let {{{ t }}} = the time in minutes to fill
14 gallon container
--------------------
(3)
Convert 2 3/4 to quarters
2 3/4 = {{{ 11/4 }}}
------------------
(4)
{{{ ( 11/4 )*t - ( 1/8)*t = 14 }}}
Multiply both sides by {{{ 8 }}}
{{{ 22t - t = 112 }}}
{{{ 21t = 112 }}}
{{{ t = 5.333 }}}
----------------
(5)
Convert {{{ 1/3 }}} min to sec
{{{ (1/3)*60 = 20 }}}
--------------------
It will take 5 min 20 sec to fill
the 14 gallon container
----------------------
(6)
check:
Convert {{{ 5.333 }}} to thirds
{{{ 5.333 = 16/3 }}}
-----------------
{{{ ( 11/4 )*t - ( 1/8)*t = 14 }}}
{{{ ( 11/4 )*( 16/3 ) - ( 1/8)*( 16/3 ) = 14 }}}
Multiply both sides by {{{ 24 }}}
{{{ 22*16 - 16 = 14*24 }}}
{{{ 352 - 16 = 336 }}}
{{{ 336 = 336 }}}
OK