Question 1036417
David's rate of working:
[ 1 job ] / [ 15 days ]
Ken's rate of working:
[ 1 job ] / [ 10 days ]
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Add their rates of working to get their
rate working together
{{{ 1/15 + 1/10 = 2/30 + 3/30 }}}
{{{ 2/30 + 3/30 = 5/30 }}}
{{{ 5/30 = 1/6 }}}
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Their rate working together is:
[ 1 job ] / [ 6 days ]
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In 2 days, the fraction of the job completed is 
{{{ 2*( 1/6 ) = 1/3 }}}
That means there is {{{ 2/3 }}} of the job left
after 2 days
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Ken leaves after 2 days.
Let {{{ t }}} = time in days for David to finish the job
{{{ 1/15 = (( 2/3 )) / t }}}
{{{ 1/15 = 2/( 3t ) }}}
Multiply both sides by {{{ 15t }}}
{{{ t = 10 }}}
David takes 10 days to finish the job
{{{ 2 + 10 = 12 }}}
The entire job takes 12 days to finish