Puzzle ZIMH 

Workings

Hint
It doesn't matter how far it was to Manchester.

Answer
Billie.

Reasoning
If we call the total distance T, we know that:

   on the way there Alex drove 90 miles, and Billie drove T – 90 miles.

   on the way back Alex drove T – 100 miles, and Billie drove 100 miles.

So, in total:

   Alex drove 90 + (T – 100) = T – 10.

   Billie drove (T – 90) + 100 = T + 10.

So Billie drove 20 miles more than Alex.