Question 1152113
Let {{{ t }}} = time to fill pool with Jim's alone
{{{ t - .7t }}} = time to fill pool with Bob
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Add their rates of filling to get rate filling together
{{{ 1/t + 1/( t - .7t ) = 1/18 }}}
Multiply both sides by {{{ t*( .3t )*18 }}}
{{{ 18*( .3t ) + 18t = t*( .3t ) }}}
{{{ 5.4t + 18t = .3t^2 }}}
{{{ .3t^2 - 23.4t = 0 }}}
{{{ t*( .3t - 23.4 ) = 0 }}}
{{{ .3t = 23.4 }}}
{{{ t = 78 }}}
and
{{{ .3t = .3*78 }}}
{{{ .3t = 23.4 }}}
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Bob's hose alone takes 23.4 hrs
Jim's hose alone takes 78 hrs
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check:
{{{ 1/t + 1/( t - .7t ) = 1/18 }}}
{{{ 1/78 + 1/23.4 = 1/18 }}}
{{{ .0128205 + .042735 = .055556 }}}
{{{ .0555555 = .055556 }}}
close enough