Question 1155962




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] = 1/7 }}}

Note that {{{ 1/7 }}} is ( 1 tub full ) / ( 7 min )

{{{ r[c] = 1/9}}}

{{{ 1/9 + r[h] = 1/7 }}}

{{{ r[h] = 1/7 - 1/9 }}}

{{{ r[h] = 9/63 - 7/63 }}}

{{{ r[h] = 2/63 }}}

{{{ r[h] = 1/31.5 }}}

With just the hot faucet open the tub fills in {{{highlight(31.5)}}} min

check:

{{{ 1/9 + 1/31.5 = 1/7 }}}
{{{ 0.14285714285714285 = 0.14285714285714285 }}}
{{{ 0.143 = 0.143 }}}