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.

Question

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.
Answer, -5.8-(-1.6)=-4.2

GPT-4o mini · Answer

To find the change in air temperature from 9 a.m. to noon, we can set up the equation as follows:

Let \( T_1 \) be the temperature at 9 a.m. and \( T_2 \) be the temperature at noon.

Given:

\( T_1 = -5.8 \) degrees Celsius (temperature at 9 a.m.)
\( T_2 = -1.6 \) degrees Celsius (temperature at noon)

The change in temperature \( \Delta T \) can be calculated by subtracting \( T_1 \) from \( T_2 \):

\[ \Delta T = T_2 - T_1 \]

Substituting the values:

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

When you simplify this, note that subtracting a negative is the same as adding:

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

Now, you can perform the calculation:

\[ \Delta T = 4.2 \]

Thus, the change in temperature is \( 4.2 \) degrees Celsius.

Explanation of the Answer:

The positive change of \( 4.2 \) degrees Celsius indicates that the temperature increased during the three-hour period from 9 a.m. to noon. This means that the air temperature became warmer, rising from a chilly -5.8 degrees Celsius to a less frigid -1.6 degrees Celsius.