Pre-calculus average rate of change word problem! help!?

Question

Suppose that between 2000 and 2005, a person's salary increases at an average rate of $2600 per year. 
Then, between 2005 and 2009, the person's salary increases at an average rate of $1800 per year. 
What is the average rate of change in salary between 2000 and 2009? 


I know that the answer is 2244.44 per year, but I don't know the process.

Answer 1

The average rate of the increase salary between 2000 to 2005 is 2600 dollars./year

Increase salary between 2000 to 2005 = ($2600)(2005 - 2000).

                                                                        =$2600*5 = $13000.

The average rate of the increase salary between 2005 to 2009 is 1800 dollars/year.

Increase salary between 2005 to 2009 = ($1800)(2009 - 2005).

                                                                        =$1800*4 = $7200.

Total increase salary between 2000 to 2009 = $13000 + $7200 = $20200.

Calculate the average rate of the increase salary between 2000 to 2009.

Average rate=Total increase salary/Number of years

                       =$20200/(2009-2000)

                       =20200/9

                        =$2244.44