Distance, Rate, Time, Average Speed word problem

Question

Michael and Andrew took turns driving on a road trip, driving the same amount of time per turn. In the same time it took Andrew to drive 150 miles, Michael covered 205 miles. Given that Michael's average cruising speed was 22 mph faster than Andrew's, find each of their average driving speeds.

Find each of their average driving Speeds

Set up and equation and define relevant variables

Answer 1

150 = r*t

 

205 = (r+22)*t = rt + 22t <--- distributive

 

                        =  150 + 22t <--- substitutes Andrews distance = rt

 

  55 = 22t

 

t = 55/22 = 5/2 = 2.5 hours

 

150 = 2.5*r ---> 150/2.5 = 60 mph

 

205 = 2.5 * (r+22)

 

205/2.5 = r+22

 

82 = r + 22

r=60

 

Andrew 60 mph

Michael 82 mph