Question 607135
Add the rates of filling and subtract the
rate of emptying
A's rate: ( 1 tank filled ) / ( 4 hrs )
B's rate: ( 1 tank filled ) / ( C's rate minus 9 hrs )
C's rate: ( 1 tank emptied ) / ( x hrs )
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When all 3 pipes are open, it takes 2 hrs to fill the tank.
{{{ 1/4 + 1/( x-9 ) - 1/x = 1/2 }}}
Multiply both sides by {{{ 4*x*( x-9 ) }}}
{{{ x*( x-9 ) + 4c - 4*( x-9 ) = 2*x*( x-9 ) }}}
{{{ x^2 - 9x + 4x - 4x + 36 = 2x^2 - 18x }}}
{{{ x^2 - 9x = 2x^2 - 18x - 36 }}}
{{{ x^2 - 9x - 36 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -9 }}}
{{{ c = -36 }}}
{{{ x = (-(-9) +- sqrt( (-9)^2 - 4*1*(-36) )) / (2*1) }}}
{{{ x = ( 9 +- sqrt( 81 + 144 )) / 2 }}}
{{{ x = ( 9 +- sqrt( 225 )) / 2 }}}
{{{ x = ( 9 + 15) / 2 }}}
{{{ x = 24/2 }}}
{{{ x = 12 }}} ( ignore the negative square root )
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If A and B are closed, C can empty the tank in 12 hrs