Question 1050064
The rate of emptying the lake is:
[ 1 lake emptied ] / [  8 wks ] 
I will call emptying a negative rate, so
this rate is {{{ -1/8 }}}
-----------------------------------
The rate of filling the lake is:
[ 1 lake filled ] / [ 15 wks ]
This is a positive rate of {{{ 1/15 }}}
--------------------------------
Let {{{ t }}} = time in weeks to empty lake
Add the given rates to get a total
negative rate of emptying of {{{ -1/t }}}
-------------------------------------
{{{ -1/8 + 1/15 = -1/t }}}
Multiply both sides by {{{ 8*15t }}}
{{{ -15t + 8t = -8*15 }}}
{{{ -7t = -120 }}}
{{{ t = 17 + 1/7 }}}
it will take 17 weeks and 1 day to empty the lake
--------------------
check:
{{{ -1/8 + 1/15 = -1/(120/7) }}}
{{{ -15/120 + 8/120 = -7/120 }}}
{{{ -7/120 = -7/120 }}}
OK