Question 898080
Add their rates of filling to get their
rate filling together
1st pipe's rate:
( 1 tank ) / ( x hrs )
2nd pipe's rate:
( 1 tank ) / ( x + 3 hrs )
Rate with both pipes filling:
( 1 tank ) / ( 2 hrs )
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{{{ 1/x + 1/( x + 3 ) = 1/2 }}}
Multiply both sides by {{{ x*( x + 3 )*2 }}}
{{{ 2*( x+3 ) + 2x = x*( x+3 ) }}}
{{{ 2x + 6 + 2x = x^2 + 3x }}}
{{{ x^2 - x - 6 = 0 }}}
{{{ ( x - 3 )*( x + 2 ) = 0 }}} ( by inspection )
{{{ x = 3 }}} is the positive answer, so
{{{ x + 3 = 6 }}}
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The 1st pipe takes 3 hrs
The 2nd pipe takes 6 hrs
----------------------
check:
{{{ 1/x + 1/( x + 3 ) = 1/2 }}}
{{{ 1/3 + 1/6 = 1/2 }}}
{{{ 2/6 + 1/6 = 3/6 }}}
{{{ 3/6 = 3/6 }}}
OK