SOLUTION: I drove to my parents' house at $40$ miles per hour. If I had driven 30 miles an hour instead, then I would have gotten there 20 minutes later. How many miles did I drive?

Algebra ->  Equations -> SOLUTION: I drove to my parents' house at $40$ miles per hour. If I had driven 30 miles an hour instead, then I would have gotten there 20 minutes later. How many miles did I drive?      Log On


   

Question 1151193: I drove to my parents' house at $40$ miles per hour. If I had driven 30 miles an hour instead, then I would have gotten there 20 minutes later. How many miles did I drive?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
SPEED           TIME         DISTANCE

40              d/40           d

30              d/30           d

difference      1/3

Twenty minutes is one-third of an hour.

d%2F30-d%2F40=1%2F3

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The solution method shown by tutor @josgarithmetic is a perfectly good standard algebraic method.

If you are one of many who dislike working with fractions, here is a very different, somewhat informal method.

The ratio of the two speeds is 40:30 = 4:3; since the distances are the same, the ratio of the times is 3:4.

Given that ratio of times, let the two times be 3x and 4x. The difference, 4x-3x=x, is 20 minutes.

That means the amount of time at 40mph was 3x = 3(20 minutes) = 60 minutes = 1 hour. And 40mph for 1 hour makes the distance 40 miles.