Ben drinks tea at an incredible rate. He drinks $3\frac{1}{2}$ liters of tea every $\frac{2}{3}$ of an hour. Ben drinks tea at a constant rate.How many liters of tea does he drink in one hour?

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Q. Ben drinks tea at an incredible rate. He drinks

3\frac{1}{2}

liters of tea every

\frac{2}{3}

of an hour. Ben drinks tea at a constant rate.How many liters of tea does he drink in one hour?

Understand the problem: First, let's understand the problem. Ben drinks $3\frac{1}{2}$ liters of tea every $\frac{2}{3}$ of an hour. We need to find out how many liters of tea he drinks in one full hour.
Calculate tea consumption rate: To find out how much tea Ben drinks in one hour, we need to calculate the rate of his tea consumption per hour. We know that he drinks $3$ and $\frac{1}{2}$ liters in $\frac{2}{3}$ of an hour. We can express $3$ and $\frac{1}{2}$ as an improper fraction, which is $\frac{7}{2}$ liters.
Set up proportion: Now, we will set up a proportion to find out how many liters he drinks in one hour. We have the ratio of $\frac{7}{2}$ liters to $\frac{2}{3}$ hours, and we want to find the number of liters per $1$ hour. The proportion is $\left(\frac{7}{2}\right) / \left(\frac{2}{3}\right) = \frac{x}{1}$ , where $x$ is the number of liters Ben drinks in one hour.
Solve for x: To solve for x, we multiply both sides of the equation by $1$ hour to isolate $x$ . This gives us $x = \frac{7}{2} / \frac{2}{3}$ . To divide by a fraction, we multiply by its reciprocal. So, $x = \frac{7}{2} \times \frac{3}{2}$ .
Perform multiplication: Multiplying the numerators together, we get $7 \times 3 = 21$ . Multiplying the denominators together, we get $2 \times 2 = 4$ . So, $x = \frac{21}{4}$ .
Simplify the fraction: The fraction $\frac{21}{4}$ can be simplified to $5$ and $\frac{1}{4}$ , or $5.25$ in decimal form. This is the number of liters Ben drinks in one hour.