Question

in which story could you use the quotient -\frac{1}{2} \div 60 to answer the question? an hourglass contains \frac{1}{2} of a cup of sand. when it is flipped over, it takes 60 minutes for the sand to completely fall from the top bulb to the bottom bulb. how much does the amount of sand in the top bulb change per minute on average? an hourglass contains \frac{1}{2} of a cup of sand. when it is flipped over, it takes 60 minutes for the sand to completely fall from the top bulb to the bottom bulb. how much does the amount of sand in the bottom bulb change per minute on average?

Explanation:

Step1: Analyze the first - story

The amount of sand in the top - bulb is decreasing. The initial amount of sand in the top - bulb is $\frac{1}{2}$ cup and it takes 60 minutes to empty. The rate of change of the amount of sand in the top - bulb is the change in the amount of sand (negative because it's decreasing) divided by the time. The change in the amount of sand in the top - bulb is $-\frac{1}{2}$ cup over 60 minutes. So the rate of change of the amount of sand in the top - bulb per minute is $-\frac{1}{2}\div60$.

Step2: Analyze the second - story

The amount of sand in the bottom - bulb is increasing. The initial amount of sand in the bottom - bulb is 0 and it ends up with $\frac{1}{2}$ cup in 60 minutes. The rate of change of the amount of sand in the bottom - bulb per minute is $\frac{1}{2}\div60$.

Answer:

The first story (An hourglass contains $\frac{1}{2}$ of a cup of sand. When it is flipped over, it takes 60 minutes for the sand to completely fall from the top bulb to the bottom bulb. How much does the amount of sand in the top bulb change per minute on average?)