Question 1101866
Man's rate is:
[ 1 job ] / [ 10 hrs ]
Younger son's rate is:
[ 1 job ] / [ 12 hrs ]
Let older son's rate =
[ 1 job ] / [ t hrs ]
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Let {{{ x }}} = the fraction of the 
job man and younger son get done
in 1 hr
Add their rates to get rate working together
{{{ 1/10 + 1/12 = x/1 }}}
Multiply both sides by {{{ 60 }}}
{{{ 6 + 5 = 60x }}}
{{{ 60x = 11 }}}
{{{ x = 11/60 }}} is the fraction that gets done.
There is {{{ 49/60 }}} of the job left to do
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{{{ 1/10 + 1/12 + 1/t = (( 49/60 ))/3 }}}
{{{ 1/10 + 1/12 + 1/t = 49/180 }}}
Multiply both sides by {{{ 180t }}}
{{{ 18t + 15t + 180 = 49t }}}
{{{ 33t + 180 = 49t }}}
{{{ 16t = 180 }}}
{{{ t = 11.25 }}}
Working alone, the older son
can do the job is 11 hrs 15 min
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