# Thread: Solving a Distance Problem

1. ## Solving a Distance Problem

I'm having a fairly hard time creating an equation from the information given to complete this problem. Here it is.

"On a vacation, Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities if his total traveling time was 32 hr."

So we have two rates & times: 50 mph at x hours and 55 mph at (32-x) hours.

anyone know where to start?

2. ## Re: Solving a Distance Problem

Originally Posted by street1030
So we have two rates & times: 50 mph at x hours and 55 mph at (32-x) hours.
And these two distances are equal.

3. ## Re: Solving a Distance Problem

Yes that also. Let's see here.

50x = 55(32-x)
50x = 1760 - 55x
105x = 1760
x = 16.76

Then

50 (16.76) + 55 (32 - 16.76) = d
50 (16.76) + 55 (15.24) = d
838 + 838 = d
d = 1676

Did I do it?

4. ## Re: Solving a Distance Problem

You found x correctly, but each of 50 (16.76) and 55 (32 - 16.76) and not the sum of them is the distance from Denver to Minneapolis. That's why you equated them. So, 1676 is the double distance.