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.

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