Answer:
[tex]\frac{350}{11} weeks[/tex]
Step-by-step explanation:
Let V be the volume of water in the lake and w be the number of weeks to empty the lake
Since it takes 14 weeks to empty the lake by water release, the empty rate = V/14
But at the same time the river is replenishing the lake at a rate of V/25 since it will take 25 weeks to fill the empty lake
- Net empty rate = Empty rate - replenishment rate = [tex]\frac{V}{14} - \frac{V}{25} = \frac{V}{w}[/tex]
- Divide the equation by V to eliminate V giving
[tex]\frac{1}{14} - \frac{1}{25} = \frac{1}{w}[/tex]
- Multiply by 350 (14 x 25) to eliminate the denominators
[tex]25 - 14 = \frac{350}{w}[/tex] ==> [tex]11 = \frac{350}{w}[/tex]
- Multiply both sides by w to cancel the denominator w
11w = 350
- Divide both sides by 11 to get
w = [tex]\frac{350}{11 }[/tex] weeks
