DeAngelo is training for a half marathon. Today he is running 13.25 miles. He jogs for the first half hour at a rate of 5.5 miles per hour, then increases his pace to p miles per hour for 1.5 hours. Write an equation representing this situation, and complete the statement that follows.__+__ p = ___DeAngelo's rate for the last 1.5 hours of his run is ___ miles per hour.

For this case, the first thing we must do is define a variable.
 We have then:
 p: rate in miles per hour for the last 1.5 hours
 We now write the equation that models the problem.
 We have then:
 [tex](0.5) * (5.5) + 1.5p = 13.25 [/tex]
 Rewriting we have:
 [tex]2.75 + 1.5p = 13.25 [/tex]
 From here, we clear the value of p.
 We have then:
 [tex]1.5p = 13.25 - 2.75 p = 10.5 / 1.5 p = 7[/tex]
 Answer:
 DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour.