Question 979547
Add the rates of filling
Rate for pipe:
[ 1 pool ] / [ 15 hrs ]
Rate for hose:
[ 1 pool ] / [ 23 hrs ]
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Let {{{ t }}} = time to fill pool {{{ 3/5 }}} full
{{{ 1/15 + 1/23 = ((3/5))/t }}}
{{{ 1/15 + 1/23 = 3/(5t) }}}
Multiply both sides by {{{ 15*23t }}}
{{{ 23t + 15t = 3*3*23 }}}
{{{ 38t = 207 }}}
{{{ t = 5.447 }}}
The pool will be 3/5 full in 5.447 hrs
check:
{{{ 1/15 + 1/23 = (3/5)/t }}}
{{{ .066667 + .043478 = .6/t }}}
{{{ .110145 = .6/t }}}
{{{ t = .6/.110145 }}}
{{{ t = 5.44735 }}}
OK