Question

The temperature at 2 A.M. was -5.5°C. The temperature changed an average of -2.1°C each hour for 4 hours and then changed an average of 3.2°C each hour for 3 hours. What was the temperature at 9 A.M.?

Answer 1

To obtain the temperature at 9A.M., the following steps are necessary:

Step 1: Find the total temperature change at the end of the 4 and 3 hour periods, as follows:

At the end of 4 hours, the total temperature change is:

`\text{total temperature change = average temperature }*\text{ nu}mber\text{ of hours}`

Thus:

`\begin{gathered} \text{total temperature change = -2.1}*\text{4} \\ \Rightarrow\text{total temperature change = }-8.4^oC \end{gathered}`

Thus, after 4 hours, the temperature that was initially at -5.5 degrees celsius at 2 A.M. becomes:

`f\text{inal temperature - initial temperature = total temperature change}`

Thus, after 4hours, that is when it is 6 A.M, the temperature is:

`\begin{gathered} f\text{inal temperature - initial temperature = total temperature change} \\ \Rightarrow finaltemperature-(-5.5^oC\text{) = }-8.4^oC \\ \Rightarrow finaltemperature\text{ = }-8.4^oC+(-5.5^oC\text{)} \\ \Rightarrow finaltemperature\text{ = }-8.4^oC-5.5^oC \\ \Rightarrow finaltemperature\text{ = }-13.9^oC \end{gathered}`

Thus, at 6 A.M (after 4 hours) the temperature is -13.9 degrees celsius.

--Finally, we find the temperature at 9 A.M. (after another 3 hours), as follows:

At the end of another 3 hours, the total temperature change is:

`\text{total temperature change = average temperature }*\text{ nu}mber\text{ of hours}`

Thus:

`\begin{gathered} \text{total temperature change = 3.2}*\text{ 3} \\ \Rightarrow\text{total temperature change =9}.6^oC \end{gathered}`

After another 3 hours, the temperature that was initially at -13.9 degrees celsius at 6 A.M. becomes the following at 9 A.M:

`\begin{gathered} f\text{inal temperature - initial temperature = total temperature change} \\ \Rightarrow f\text{inal temperature - }(-13.9^oC\text{) = 9.6}^oC \\ \Rightarrow f\text{inal temperature = 9.6}^oC+(-13.9^oC\text{)} \\ \Rightarrow f\text{inal temperature = 9.6}^oC-13.9^oC \\ \Rightarrow f\text{inal temperature = -4.3}^oC \end{gathered}`

IN CONCLUSION, therefore, the temperature at 9 A.M is - 4.3 degree celsius