Question 786580
I don't use tables, but my equations can 
easily be put into a table
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Add their rates to get rate working together
Jen's rate: ( 1 cart ) / ( x min )
Pat's rate: ( 1 cart ) / (  x - 12 min ) 
Together: ( 1 cart ) / ( 100 min )
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{{{ 1/x + 1/( x-12 ) = 1/100 }}}
Multiply both sides by {{{ x*( x-12 )*100 }}}
{{{ 100*(x-12) + x*100 = x*( x-12 ) }}}
{{{ 100x - 1200 + 100x = x^2 - 12x }}}
{{{ x^2 - 212x + 1200 = 0 }}}
Use quadratic formula
{{{ x = ( -b +- sqrt( b^2-4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -212 }}}
{{{ c = 1200 }}}
{{{ x = ( -(-212) +- sqrt( (-212)^2-4*1*1200 )) / (2*1) }}}
{{{ x = ( 212 +- sqrt( 44944 -4800 )) / 2 }}}
{{{ x = ( 212 +- sqrt( 40144 )) / 2 }}}
{{{ x = ( 212 + 200.36 ) / 2 }}}
{{{ x = 412.36/2 }}}
{{{ x = 206.18 }}}
In hours:
{{{ 206.18 / 60 = 3 + 26.18/60 }}}
It would take Jen 3 hrs and 26 min
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check:
{{{ x - 12 = 206.18 - 12 }}}
{{{ x - 12 = 194.18 }}}
{{{ 1/x + 1/( x-12 ) = 1/100 }}}
{{{ 1/206.18 + 1/194.18 = 1/100 }}}
{{{ .00485 + .00515 = .01 }}}
{{{ .01 = .01 }}}
OK