Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 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

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it empties the lake in 10 weeks and a river (with rate can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

which implies that this rate empties 0.1 of the lake per week, thus, .

Using the same idea, we can obtain that the filling rate of the river is:

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

, which means that the lake is being empty at a rate of -0.05 week and using the rule of three:

Thus, It takes 20 weeks to empty the lake.

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