One day at 3 a. m. the temperature was -13 in klondike alaska at 10 am it was 22 degrees . what was the average change in temperature per hour

The average change of temperature per hour is the difference in temperature divided by the difference in hours.

3 a.m.     10 a.m.  > difference in time: 10 - 3 = 7
-13           22         > difference in temperature: 22 - (-13) = 35

average change of temperature per hour: 35/7 = 5

5 degrees per hour

Comment
You are moving a total from - 13  to + 22. That alone is enough to make someone wonder why they live where they live. (The weather where I live can can do exactly this). 

What is the range of the temperature?
You might think it was -13 to 22. It sounds like it could be 9 degrees. 22 - 13 = 9. 

That is not right. The actual movement is absolute value of (-13) which will be added onto 22.

So the temperature movement is
13 + 22 = 35 degrees.

Hours.
The hours are not as hard to figure out. From 3am to 10 am is 7 hours

Degrees per hour
Formula 
Degrees / hour = degrees / hour
degrees = 35 degrees
hour = 7 hours.

Degrees / hour = 35 degrees / 7 hours = 5 degrees / hour.