Here is how I set it up:

Let X = Total miles

X/2 = Half of the trip

Then she drove 1/4 of the remaining trip so: 1/4 * x/2 = x/8

So at this point we know she drove X/2 miles. Took a break. Then drove X/8 miles and took a break. The remaining miles are 120 so...

X/2 - X/8 = 120

3X/8 = 120

3X = 960

X=320


You could plug in and work backward on this problem also.

Start with 320 Miles

You drive half of the trip

That means you drove 160.

Then you drive 1/4 of the 160. So you drive 40 miles.

160 - 140 = 120 miles left

Another approach:

Let x be the total distance

x/2+ x/8+120 = x

x=320