Question

An apple-juice container has a tiny hole in it, so it is slowly leaking. if the container leaks three ounces every 19 minutes, how long will it take for the 16 ounces of juice in the container to leak out? write a proportional equation and solve with j.r.'s strategy of using a giant one.

Answer 1

101 1/3 minutes

Explanation:

You want to find the time for leaking 16 ounces of juice, given that leaking 3 ounces takes 19 minutes.

Proportion

Writing the proportion as time (minutes)/volume (ounces), we have ...

t/16 = 19/3

Solution

To solve this "using a giant one" we can use 1 = 3/3 on the left, and 1 = 16/16 on the right.

`(t)/(16)*(3)/(3)=(19)/(3)*(16)/(16)\\\\\\(3t)/(48)=(304)/(48)\\\\\\3t=304\qquad\text{equate numerators}\\\\\\t=(304)/(3)=101(1)/(3)\qquad\text{divide by 3}`

It will take 101 1/3 minutes for the juice to leak out.

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Additional comment

The method of "using a giant one" does not work well here, because the numbers in one proportion are not a simple multiple of the numbers in the other.

For this proportion, a better strategy is to multiply both sides by the denominator of the variable: 16. After the multiplications and division, that is effectively what we accomplished using more steps.

We could have used a "giant one" that was (16/3)/(16/3), and we would have gotten the same result: t = (19)(16/3).

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