Question

how many weeks does it take to empty the lake?

Answer 1

The rate of emptying the lake is -1/8.

The rate of filling the lake is 1/15

Let t be the time in weeks to empty the lake,

Now, add the given rate to get the total rate of emptying of -1/t.

$\begin{gathered} \frac{-1}{8}+\frac{1}{15}=-\frac{1}{t} \\ \frac{-15+8}{120}=-\frac{1}{t} \\ -7\times t=-120 \\ t=\frac{120}{7} \end{gathered}$

Thus,

$t=17\frac{1}{7}$

Therefore, it will take 17 weeks and 1 day to empty the lake.