Abdul drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when abdul drove home, there was no traffic and the trip only took 4 hours. if his average rate was 27 miles per hour faster on the trip home, how far away does abdul live from the mountains?

So let's call the rate abdul went on the 7 hour trip, x. Then we can say he went x +27 on the 4 hour trip. We can then say that time times rate equals distance and make 7*x = d and 4*(x+27) = d as valid equations, where d is our total distance. We can set the equations equal to get 4x + 108 = 7x, so x = 36. Then we can plug that into the first equation to get the total distance d = 7(36) = 252 miles.