Question

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 12 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:

30 weeks

Explanation:

Time taken to empty the lake = 12 weeks

Time taken to replenish the lake = 20 weeks

Job per week to empty the lake = 1/12

Job per week to fill the lake = 1/20

Let x be the time it takes to do both of these activities at the same time

$\frac{1}{12}-\frac{1}{20}=\frac{1}{x}\\\Rightarrow \frac{5-3}{60}=\frac{1}{x}\\\Rightarrow x=\frac{60}{2}\\\Rightarrow x=30\ weeks$

Time it takes to do both of these activities at the same time is 30 weeks.