Bill and Joe leave their house at the same time heading in opposite directions. If Bill is driving three times faster than Joe and it takes them three hours to be 120 miles apart, how fast is Bill driving?

The problem statement gives you the relationship between their speeds, and it gives you information you can use to find their total speed. You solve this by finding the total speed, then the proportion of that belonging to Bill.

The total speed is (120 mi) / (3 h) = 40 mi/h.

The speed ratio is ...

... Bill : Joe = 3 : 1

so the speed ratio Bill : Total is ...

... 3 : (3+1) = 3:4.

Bill's speed is (3/4) * (40 mi/h) = 30 mi/h.