Question 796733
Let {{{ t }}} = time in hrs for Sam to paint building alone
Margaret's rate: ( 1 building ) / ( 5 hrs )
Margaret and Sam together: ( 1 building ) / ( 3 hrs )
-------------
Add their rates to get rate working together
{{{ 1/5 + 1/t = 1/3 }}}
Multiply both sides by {{{ 15t }}}
{{{ 3t + 15 = 5t }}}
{{{ 2t = 15 }}}
{{{ t = 7.5 }}}
-----------
Sam can paint the building alone in 7.5 hrs
check:
{{{ 1/5 + 1/t = 1/3 }}}
{{{ .2 + 1/7.5 = .333 }}}
{{{ .2 + .1333 = .333 }}}
{{{ .333 = .333 }}}
OK