Question

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 20 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

Answer 1

Answer:$\frac{140}{3}$ weeks

Step-by-step explanation:

Given

It takes 14 weeks to empty a lake

also it takes 20 weeks for a river to fill the lake

Part of lake empty in 1 week $=\frac{1}{14}$

Part of lake filled in 1 week is $=\frac{1}{20}$

And if both works simultaneously then

$\frac{1}{14}-\frac{1}{20}=\frac{10-7}{140}$

$=\frac{3}{140}$

therefore it takes $\frac{140}{3}$ weeks to fill it