Question 1108519
What fraction of the job does 1st painter
get done in 3 days?
His rate of painting is [ 1 building ] / [ 15 days ]
{{{ (1/15)*3 = 1/5 }}}
That means there is {{{ 4/5 }}} of the building
left to paint
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Add their rates of painting to get their rate
painting together
Let {{{ t }}} = their time in days to paint {{{ 4/5 }}}
of the building working together
{{{ 1/15 + 1/10 = ((4/5))/t }}}
Multiply both sides by {{{ 30t }}}
{{{ 2t + 3t = 24 }}}
{{{ 5t = 24 }}}
{{{ t = 4.8 }}}
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Add the 3days to 4.8 days
{{{ 3 + 4.8 = 7.8 }}}
It takes 7.8 days to paint the building
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check the math & get a 2nd opinion if needed