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

Answer 1

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.