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 know is the following definition:
 d = v * t
 Where,
 d: distance
 v: speed
 t: time
 Therefore, the total distance traveled in this case is:
 (5.5) * (0.5) + (1.5) * p = 13.25
 Rewriting:
 2.75 + 1.5p = 13.25
 Clearing the value of p we have:
 p = (13.25-2.75) / (1.5)
 p = 7
 
 an equation representing this situation is:
 2.75 + 1.5p = 13.25
 DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour