QuestionFelipe drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Felipe drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Felipe live from the mountains?
Do not do any rounding.

Studdy Solution
Solve the system of equations to find the distance.
First, expand the equation: $$8r = 6r + 96$$
Subtract $6r$ from both sides to isolate terms with $r$: $$2r = 96$$
Divide both sides by 2 to solve for $r$: $$r = 48$$
Now, substitute $r = 48$ back into the equation for distance: $$d = r \times 8 = 48 \times 8$$
Calculate the distance: $$d = 384$$
The distance from Felipe's home to the mountains is: $$\boxed{384}$$