Idrove to my parents' house at 60 miles per hour. if i had driven 50 miles an hour instead, then i would have gotten there 40 minutes later. how many miles did i drive?

Use distance = rate x time

Let "t" be the time it took for you to drive to your parent's house at 60mph.

So 60t would be the distance.

And "t+40" would be the time it took for you to get to your parent's house at 50 mph.  And that total distance would be 50(t+40).

Since both the distances are the same, this gives us the equation:

60t = 50(t+40)

Simplify:  60t = 50t + 2000
10t = 2000
t = 200 minutes

Driving at 60 mph for 200 minutes equates to a total distance of 200 miles.