Question 798797
Let {{{ r[c] }}} = the rate of filling with cold water faucet alone
Let {{{ r[h] }}} = the rate of filling with hot water faucet alone
{{{ r[c] + r[h] = 1/9 }}}
Note that {{{ 1/9 }}} is ( 1 tub full ) / ( 9 min )
{{{ r[c] = 1/15 }}}
{{{ 1/15 + r[h] = 1/9 }}}
{{{ r[h] = 1/9 - 1/15 }}}
{{{ r[h] = 5/45 - 3/45 }}}
{{{ r[h] = 2/45 }}}
{{{ r[h] = 1/22.5 }}}
With just the hot faucet open the tub fills in 22.5 min
check:
{{{ 1/15 + 1/22.5 = 1/9 }}}
{{{ .0667 + .0444 = .1111 }}}
{{{ .1111 = .1111 }}}
OK