Question

in which story could you use the quotient -\frac{1}{2}\div60 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 change in top - bulb sand

The amount of sand in the top bulb is decreasing. The total decrease is $\frac{1}{2}$ cup in 60 minutes. To find the rate of change per minute, we use the formula for average rate of change, which is $\text{Rate}=\frac{\text{Change in quantity}}{\text{Time}}$. Here, the change in the amount of sand in the top bulb is $-\frac{1}{2}$ (negative because it is decreasing) and the time is 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 change in bottom - bulb sand

The amount of sand in the bottom bulb is increasing. The total increase is $\frac{1}{2}$ cup in 60 minutes. The rate of change of the amount of sand in the bottom bulb per minute is $\frac{1}{2}\div60$ (positive because it is increasing).

Answer:

The story about the change in the amount of sand in the top bulb.