The temperature falls from 0 degrees to Negative 12 and one-fourth degrees in 3 and one-half hours. Which expression finds the change in temperature per hour?

Negative StartFraction 7 over 2 EndFraction divided by StartFraction 49 over 4 EndFraction
Negative StartFraction 7 over 2 EndFraction times StartFraction 49 over 4 EndFraction
Negative StartFraction 49 over 4 EndFraction times StartFraction 7 over 2 EndFraction
Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction

1 answer

To find the change in temperature per hour, we first need to determine the total change in temperature and the total time in hours.

  1. Calculate the change in temperature:

    The temperature changes from 0 degrees to -12.25 degrees (which is -12 and one-fourth degrees). The change in temperature is calculated as follows:

    \[ \text{Change in temperature} = \text{final temperature} - \text{initial temperature} = -12.25 - 0 = -12.25 \text{ degrees} \]

  2. Calculate the total time:

    The total time given is 3.5 hours.

  3. Calculate the change in temperature per hour:

    We can express the change in temperature per hour as:

    \[ \text{Change in temperature per hour} = \frac{\text{Change in temperature}}{\text{Total time}} = \frac{-12.25}{3.5} \]

    To simplify further, we can convert -12.25 and 3.5 into fractions: \[ -12.25 = -\frac{49}{4} \quad \text{and} \quad 3.5 = \frac{7}{2} \]

    Now we can substitute these values into the expression: \[ \text{Change in temperature per hour} = \frac{-\frac{49}{4}}{\frac{7}{2}} \]

    To divide fractions, we multiply by the reciprocal: \[ = -\frac{49}{4} \times \frac{2}{7} \]

Thus, we need to identify the correct expression from the provided options. The correct expression that is equivalent to our calculation is:

  • Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction

So the answer is: \[ \text{Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction} \]