Question 1155727
Let {{{ t }}} = the time in hrs it takes Dennis to do the job
{{{ t - 2 }}} = the time in hrs it takes Michael to do the job
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Dennis's rate of working:
[ 1 job ] / [ t hrs ]
Michael's rate of working:
[ 1 job ] / [ t - 2 hrs ] 
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Add their rates of working to get their rate working together
{{{ 1/t + 1/( t-2 ) = 1/5 }}}
Multiply both sides by {{{ t*( t-2 )*5 }}}
{{{ 5*( t - 2 ) + 5t = t*( t-2 ) }}}
{{{ 5t - 10 + 5t = t^2 - 2t }}}
{{{ t^2 - 12t + 10 = 0 }}}
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Use quadratic formula
{{{ t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = -12 }}}
{{{ c = 10 }}}
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{{{ t = (-(-12) +- sqrt( (-12)^2-4*1*10 ))/(2*1) }}}
{{{ t = ( 12 +- sqrt( 144 - 40 ))/2 }}}
{{{ t = ( 12 + 10.198 )/2 }}}
{{{ t = 22.198 / 2 }}}
{{{ t = 11.099 }}}
and
{{{ t - 2 = 9.099 }}}
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Rounded off, Michael's time to do the job alone is:
9.1 hrs
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check the answer:
{{{ 1/t + 1/( t-2 ) = 1/5 }}}
{{{ 1/11.099 + 1/9.099 = 1/5 }}}
{{{ .0901 + .1099 = .2 }}}
{{{ .2009 = .2 }}}
Error due to rounding off, I believe
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Get a 2nd opinion also, if needed