Question 593460
Add their individual rates of picing to get 
their rate of picking together
Together, rate = ( 1 bushel ) / ( 16 min )
Let {{{ t }}} = Johanne's time ion minutes to pick 1 bushel
{{{ t + 4 }}} = Maria's time in minutes to pick 1 bushel
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{{{ 1/t + 1/( t + 4 ) = 1/16 }}}
Multiply both sides by {{{ 16t*( t + 4 ) }}}
{{{ 16*( t + 4 ) + 16t = t*( t + 4 ) }}}
{{{ 16t + 64 + 16t = t^2 + 4t }}}
{{{ t^2 - 32t + 4t - 64 = 0 }}}
{{{ t^2 - 28t - 64 = 0 }}}
Use quadratic formula
{{{t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = -28 }}}
{{{ c = -64 }}}
{{{ t = (-(-28) +- sqrt( (-28)^2 - 4*1*(-64) )) / (2*1) }}} 
{{{ t = ( 28 +- sqrt( 784 + 256 )) / 2 }}} 
{{{ t = ( 28 +- sqrt( 1040 )) / 2 }}} 
{{{ t = ( 28 + 32.25) / 2 }}} ( using the (-) sqrt gives negative time: ignore )
{{{ t = 60.25/2 }}}
{{{ t = 30.125 }}}
{{{ t + 4 = 34.125 }}}
Johanne takes 30.125 min picking alone
Maria takes 34.125 min picking alone
check:
{{{ 1/t + 1/( t + 4 ) = 1/16 }}}
{{{ 1/30.125 + 1/34.125 = 1/16 }}}
{{{ .0332 + .0293 = .0625 }}}
{{{ .0625 = .0625 }}}
OK