Question

Raychel drove to the mountains last week there was heavy traffic on the way there and on the trip took 12 hours when Raychel drove home there was no traffic and the trip only took eight hours if her average rate was 20 mph faster on the trip home how far away does Rachel live from the mountains

Answer 1

Suppose that this person drives at r mph going to the mountains, and gets there in 12 hours.  Returning, this person drives at (r+20) mph and gets home in 8 hours.  We don't know the distance yet, but can solve for the initial speed, r, by setting

d = 12r = (r+20)(8).  Solving for r, r=40 mph (going) and (40+20)mph = 60 mph (returning.  Since d=12 r, d = (12 hrs)(40 mph) = 480 miles (answer).