Question

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.

Answer 1

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:
 $(0.5) * (5.5) + 1.5p = 13.25$
 Rewriting we have:
 $2.75 + 1.5p = 13.25$
 From here, we clear the value of p.
 We have then:
 $1.5p = 13.25 - 2.75 p = 10.5 / 1.5 p = 7$
 Answer:
 DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour.