Question 982238
Let {{{ t |}}} = Rick's time to finish work alone in hours
{{{ t - 6 }}} = Pete's time to finish work aone in hours
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Rick's rate of working:
[ 1 job finished ] / [ t hrs ]
Pete's rate of working:
[ 1 job finished ] / [ t - 6 ]
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Convert 12 min to hrs:
{{{ 12/60 = .2 }}} hrs
Add their rates of working to get
their rate working together
{{{ 1/t + 1/( t-6 ) = 1/9.2 }}}
Multiply both sides by {{{ 9.2*t*( t-6 ) }}}
{{{ 9.2*( t-6 ) + 9.2t = t*( t-6 ) }}}
{{{ 9.2t - 55.2 + 9.2t = t^2 - 6t }}}
{{{ t^2 - 18.4t - 6t + 55.2 = 0 }}}
{{{ t^2 - 24.4t + 55.2 = 0 }}}
Use quadratic formula
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -24.4 }}}
{{{ c = 55.2 }}}
{{{ t = ( -(-24.4) +- sqrt( (-24.4)^2 - 4*1*55.2 )) / (2*1) }}}
{{{ t = ( 24.4 +- sqrt( 595.36 - 220.8 )) / 2 }}}
{{{ t = ( 24.4 +- sqrt( 374.56 )) / 2 }}}
{{{ t = ( 24.4 + 19.354 )/2 }}}
{{{ t = 43.754/2 }}}
{{{ t = 21.877 }}}
and
{{{ t - 6 = 15.877 }}}
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Rick takes 21.877 hrs working aloine
Pete takes 15.877 hrs working alone
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check:
{{{ 1/t + 1/( t-6 ) = 1/9.2 }}}
{{{ 1/21.877 + 1/15.877 = 1/9.2 }}}
{{{ .04571 + .06298 = .1087 }}}
{{{ .10869 = .1087 }}}
close enough
Hope I got it!