Question

On average, Camila drinks 2/5 of an 6-ounce glass of water in 1 1/3 hours. Howmuch water does she drink, in glasses per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

Answer 1

This questions gives us the amount Camila drinks and the time in which she drinks that water. We want to divide the amount she drinks by the time to find how many ounces of water she drinks per hour. Since the time is a mixed number, we should transform this number to a fraction, so dividing by it would be easier. Also, note that we are told that she drinks 2/5 of a 6-ounces glass, so we should calculate the amount of total ounces she drinks. Lets start with this calculation

Since she is drinking 2/5 of a 6-ounces glass, we simply multiply this fraction and 6 to find out the fraction of ounces she drinks. We get

$6\cdot\frac{2}{5}=\frac{12}{5}$

So Camila drinks 12/5 ounces of water.

Now, lets transform the mixed number of the time to a fraction, so it is easier to divide the numbers.

Recall that to transform a mixed number to a fraction, we multiply the whole number by the denominator. Then we add the numerator to this result. Finally, this last result we put it on top of the denominator we had.

So, for 1 1/3, we calculate 1*3+1 =4. Then we put this on top of the denominator, so we get

$\frac{4}{3}$

That means that Camila drinks 12/5 ounces of water in 4/3 hours. Now, we divide both numbers to get the ounces per hour ratio she drinks on average.

$\frac{\frac{12}{5}}{\frac{4}{3}}=\frac{12\cdot3}{5\cdot4}=\frac{4\cdot3\cdot3}{5\cdot4}=\frac{3\cdot3}{5}=\frac{9}{5}$

Then, Camila drinks 9/5 ounces of water per hour. To find out the number of glasses she drinks we have the equivalence that 1 glass are 6 ounces, so we multiply this number by 1/6

$\frac{9}{5}\cdot\frac{1}{6}=\frac{3\cdot3}{5\cdot3\cdot2}=\frac{3}{10}$

so she drinks 3/10 of a glass per hour