Question 723201
The question to ask is: "What fraction of the job does
Ralph get done in a 1/2 hour ?"
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Multiply Ralph's rate of painting times 1/2 hr
( 1 fence / 6 hrs ) x ( 1/2 ) = 1/12
So Ralph finishes 1/12 of the fence in 1/2 hr
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There is 11/12 of the fence left to paint
Add their rates of painting to get their rate
painting 11/12 of the fence
{{{ 1/6 + 1/10 = (11/12) / t }}}
Multiply both sides by {{{ 12t }}}
{{{ 2t + 1.2t = 11 }}}
{{{ 3.2t = 11 }}}
{{{ t = 11/3.2 }}}
{{{ t = 3.438 }}}
They must work together for 3.438 hrs to finish