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Ben drinks tea at an incredible rate. He drinks
3(1)/(2) liters of tea every
(2)/(3) of an hour. Ben drinks tea at a constant rate.
How many liters of tea does he drink in one hour?
liters

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. $\newline$ How many liters of tea does he drink in one hour? $\newline$ liters

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GCF and LCM: word problems

Full solution

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.

\newline

How many liters of tea does he drink in one hour?

\newline

liters

Identify Rate and Time Period: Identify the rate at which Ben drinks tea and the time period for that rate. $\newline$ Ben drinks $3\left(\frac{1}{2}\right)$ liters of tea every $\left(\frac{2}{3}\right)$ of an hour.
Convert Tea Consumption Rate: Convert Ben's tea consumption rate to a fraction for easier calculation. $\newline$ $3(1/2)$ liters is the same as $7/2$ liters (since $3(1/2) = 6/2 + 1/2 = 7/2$ ).
Calculate Liters in One Hour: Calculate how many liters of tea Ben drinks in one hour by setting up a proportion. $\newline$ Since Ben drinks $\frac{7}{2}$ liters in $\frac{2}{3}$ of an hour, we can find out how much he drinks in one hour by dividing the amount he drinks by the fraction of the hour he takes to drink it. $\newline$ $\left(\frac{7}{2}\right)$ liters / $\left(\frac{2}{3}\right)$ hour = $\left(\frac{7}{2}\right) \times \left(\frac{3}{2}\right)$ liters/hour
Perform Multiplication: Perform the multiplication to find the rate per hour. $\newline$ $(\frac{7}{2}) \times (\frac{3}{2}) = \frac{21}{4}$ liters per hour
Convert to Mixed Number: Convert the improper fraction to a mixed number if necessary. $\frac{21}{4}$ liters is $5\left(\frac{1}{4}\right)$ liters.

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