Question 924077
Add their rates of filling, making the rate
of emptying negative
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Pipe A:
( 1 pond filled ) / 56 hrs
Pipe B:
( 1 pond filled ( / 42 hrs
Pipe C:
( 1 pond emptied ) / 72 hrs
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Let {{{ t }}} = time in hrs to fill the pond
{{{ 1/56 + 1/42 - 1/72 = 1/t }}}
{{{ 1 / ( 7*8) + 1/(6*7) - 1/(9*8) = 1/t }}}
Multiply both sides by {{{ 6*7*8*9*t }}}
{{{ 6*9*t + 8*9*t - 6*7*t = 6*7*8*9 }}}
Divide both sides by {{{ 3 }}}
{{{ 18t + 24t - 14t = 1008 }}}
{{{ 28t = 1008 }}}
{{{ t = 36 }}}
The pond will fill in 36 hrs
check:
I can use my calculator
{{{ 1/56 + 1/42 - 1/72 = 1/36 }}}
{{{ .017857 + .023809 - .013888 = .027777 }}}
{{{ .027778 = .027777 }}}
close enough