Question 1006472
Tom's rate of working is:
[ 2/3 of fence painted ] / [ 3 hrs ]
{{{ (2/3) / 3 = 2/9 }}}
-------------------
Huck's rate of working is:
[ 1/3 of fence painted ] / [ 2 hrs ] 
{{{ (1/3) / 2 = 1/6 }}}
-----------------
Add their rates of painting to get
their rate of painting together
------------------------
Let {{{ t }}} = time in hrs for them
to paint fence working together
[ 1 fence painted ] / [ t hrs ] is their
rate working together
--------------------------
{{{ 2/9 + 1/6 = 1/t }}}
Multiply both sides by {{{ 18t }}}
{{{ 4t + 3t = 18 }}}
{{{ 7t = 18 }}}
{{{ t = 2.571 }}} hrs
This is about 2 hrs 34 min
----------------------
The portion that Huck paints is:
[ his rate ] x [ time spent painting ]
{{{ (1/6)*2.571 = .4286 }}} 
-----------------------
check answer:
{{{ 2/9 + 1/6 = 1/t }}}
{{{ 2/9 + 1/6 = 1/2.571 }}}
{{{ .2222 + .1667 = .3889 }}}
{{{ .3889 = .3889 }}}
OK