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Solve the following word problem. The air temperature at 9 a.m. is −5.8

degrees Celsius. The air temperature at noon is −1.6
degrees Celsius. What is the change in the temperature during these three hours? Write and solve an equation to show your answer. Then explain what your answer means.(4 points)

3 answers

To find the change in temperature over the three hours from 9 a.m. to noon, we can set up an equation based on the initial temperature and the final temperature.

Let:

  • \( T_{\text{initial}} = -5.8 \) degrees Celsius (temperature at 9 a.m.)
  • \( T_{\text{final}} = -1.6 \) degrees Celsius (temperature at noon)

The change in temperature (\( \Delta T \)) can be calculated using the following equation:

\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]

Now we can substitute the values into the equation:

\[ \Delta T = -1.6 - (-5.8) \]

This simplifies to:

\[ \Delta T = -1.6 + 5.8 \]

Calculating this gives:

\[ \Delta T = 4.2 \]

So, the change in temperature over those three hours is \( 4.2 \) degrees Celsius.

Explanation of the Answer:

This means that the temperature increased by \( 4.2 \) degrees Celsius from 9 a.m. to noon. Initially, the temperature was quite cold at \( -5.8 \) degrees Celsius, and by noon, it had risen to \( -1.6 \) degrees Celsius. Thus, we can conclude that there was a notable warming trend in the air temperature during this time period.

put it all together

Sure! Here’s the complete solution, all put together:

Problem Statement:

The air temperature at 9 a.m. is −5.8 degrees Celsius. The air temperature at noon is −1.6 degrees Celsius. What is the change in the temperature during these three hours? Write and solve an equation to show your answer. Then explain what your answer means.

Solution:

To determine the change in temperature from 9 a.m. to noon, we will use the following information:

  • Initial temperature at 9 a.m. (\( T_{\text{initial}} \)): \( -5.8 \) degrees Celsius
  • Final temperature at noon (\( T_{\text{final}} \)): \( -1.6 \) degrees Celsius

We can calculate the change in temperature (\( \Delta T \)) using the equation:

\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]

Substituting the values into the equation:

\[ \Delta T = -1.6 - (-5.8) \]

This simplifies to:

\[ \Delta T = -1.6 + 5.8 \]

Now, performing the calculation:

\[ \Delta T = 4.2 \]

Thus, the change in temperature over the three-hour period from 9 a.m. to noon is 4.2 degrees Celsius.

Explanation:

This result indicates that the temperature increased by 4.2 degrees Celsius from 9 a.m. to noon. Initially, the temperature was quite cold at −5.8 degrees Celsius, and by noon, it had risen to −1.6 degrees Celsius. This suggests a noticeable warming trend in the air temperature during this period.

This completes the full solution to the word problem.