Question 1136307
Add their rates of working to get rate working together:
Let {{{ t }}} = time in hrs to paint 1/2 the fence
{{{ 1/2 + 1/3 = ((1/2))/t }}}
Multiply both sides by {{{ 6t }}}
{{{ 3t + 2t = 3 }}}
{{{ 5t = 3 }}}
{{{ t = 3/5 }}}
---------------------
Then Ted paints 1/2 the fence alone.
Let {{{ t[1] }}} = his time to paint 1/2 of the fence
{{{ 1/3 = ((1/2))/t[1] }}}
Multiply both sides by {{{ 3t[1] }}}
{{{ t[1] = 3/2 }}}
---------------------
{{{ t + t[1] = 3/5 + 3/2 }}}
{{{ t + t[1] = 6/10 + 15/10 }}}
{{{ t + t[1] = 2.1 }}} hrs
convert to hrs + min
{{{ .1*60 = 6 }}} min
Total time to paint the fence is 2 hrs 6 min
---------------
Get a 2nd opinion if needed