Question 1158067
Working together, their rate of painting is:
[ 1 deck ] / [ 6 hrs ]
Let {{{ t }}} = Craig's time in hrs working alone
His rate of working is:
[ 1 deck ] / [ t hrs ]
Cindy's rate of working is:
[ 1 deck ] / [ 3t hrs ]
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Add their rates of working to get their rate working together
{{{ 1/t + 1/(3t) = 1/6 }}}
Multiply both sides by {{{ 6t }}}
{{{ 6 + 2 = t }}}
{{{ t = 8 }}}
Craig takes 8 hrs to paint the deck working alone
check:
{{{ 1/8 + 1/24 = 1/6 }}}
{{{ 3/24 + 1/24 = 4/24 }}}
OK