Question

Ben drinks tea at an incredible rate. He drinks

\[3\dfrac{1}2\] liters of tea every

\[\dfrac{2}3\] of an hour. Ben drinks tea at a constant rate.
How many liters of tea does he drink in one hour?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's first convert the mixed number to an improper fraction:

\[3\dfrac{1}{2} = \dfrac{2}{2} + \dfrac{1}{2} = \dfrac{2+1}{2} = \dfrac{3}{2}\]
So, Ben drinks $\dfrac{3}{2}$ liters of tea every $\dfrac{2}{3}$ of an hour.

To find how many liters of tea Ben drinks in one hour, we need to find the reciprocal of $\dfrac{2}{3}$ and multiply it by $\dfrac{3}{2}$.

The reciprocal of $\dfrac{2}{3}$ is $\dfrac{3}{2}$ (since $\dfrac{2}{3} \cdot \dfrac{3}{2} = 1$).

So, $\dfrac{3}{2}$ liters of tea every $\dfrac{2}{3}$ hour is equal to $\dfrac{3}{2} \cdot \dfrac{3}{2} = \dfrac{9}{4}$ liters of tea in one hour.

Therefore, Ben drinks $\boxed{\dfrac{9}{4}}$ liters of tea in one hour.