Question

Ben drinks tea at an incredible rate. He drinks 3\dfrac123 2 1 ​ 3, start fraction, 1, divided by, 2, end fraction liters of tea every \dfrac23 3 2 ​ start fraction, 2, divided by, 3, end fraction of an hour. Ben drinks tea at a constant rate.

Answer 1

He drinks 21/4, or 5 1/4, liters of tea in 1 hour

Explanation:

The following question is missing: How much does he drink in one hour?

Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:

7/2 liters / x liters = 2/3 hour / 1 hour

x = (7/2)/(2/3) = 7/2 * 3/2

x = 21/4 = 5 1/4 liters

Answer 2

`5(1)/(4)` liters per hour.

Explanation:

Consider the question: 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?

To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:

`3(1)/(2)\text{Liters}/ (2)/(3)\text{ hour}`

Convert mixed fraction into improper fraction:

`(7)/(2)\text{Liters}/ (2)/(3)\text{ hour}`

Convert division problem into multiplication problem by flipping the 2nd fraction:

`(7)/(2)\text{ Liters}* (3)/(2)\text{ hour}`

`(21)/(4)\frac{\text{ Liters}}{\text{ hour}}`

`5(1)/(4)\frac{\text{ Liters}}{\text{ hour}}`

Therefore, Ben drinks
`5(1)/(4)` liters per hour.