Nizhoni adds water at a constant rate to a $2 \mathrm{~L}$ reservoir in a water filtering pitcher until it is full. At the same time, water goes through the filter and out of the reservoir, into the pitcher. It takes $\frac{5}{11}$ minutes to fill the reservoir, then another $3 \frac{1}{3}$ minutes for the reservoir to empty. $\newline$ At what rate does Nizhoni add water to the reservoir? $\newline$ $\frac{\mathrm{L}}{\min }$

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Q. Nizhoni adds water at a constant rate to a

2 \mathrm{~L}

reservoir in a water filtering pitcher until it is full. At the same time, water goes through the filter and out of the reservoir, into the pitcher. It takes

\frac{5}{11}

minutes to fill the reservoir, then another

3 \frac{1}{3}

minutes for the reservoir to empty.

\newline

At what rate does Nizhoni add water to the reservoir?

\newline

\frac{\mathrm{L}}{\min }

Understand the problem: Understand the problem. $\newline$ We need to find out the rate at which Nizhoni adds water to the reservoir. The rate is the amount of water added per unit of time. We know the total time it takes to fill the reservoir and the volume of the reservoir.
Convert time to minutes: Convert the time to fill the reservoir into minutes. $\newline$ The time given to fill the reservoir is $(5)/(11)$ minutes. This is already in minutes, so no conversion is necessary.
Convert time to minutes: Convert the time for the reservoir to empty into minutes. $\newline$ The time given for the reservoir to empty is $3\left(\frac{1}{3}\right)$ minutes, which is $3 + \frac{1}{3}$ minutes. Converting $\frac{1}{3}$ minutes to seconds, we get $\frac{1}{3} \times 60 = 20$ seconds. So, $3\left(\frac{1}{3}\right)$ minutes is $3$ minutes and $20$ seconds. However, this information is not needed to calculate the rate at which water is added, so we will not use it in our calculations.
Calculate rate: Calculate the rate at which Nizhoni adds water to the reservoir. $\newline$ The volume of the reservoir is $2$ liters, and the time taken to fill it is $(5)/(11)$ minutes. The rate is volume divided by time, so the rate is $2$ liters / $(5/11)$ minutes.
Perform division: Perform the division to find the rate. $\newline$ To find the rate, we divide $2$ liters by $(5/11)$ minutes. This is the same as multiplying $2$ liters by the reciprocal of $(5/11)$ minutes, which is $11/5$ . So, the rate is $2 \times (11/5) = 22/5$ liters per minute.
Simplify rate: Simplify the rate. $\frac{22}{5}$ liters per minute simplifies to $4.4$ liters per minute.