Puzzle ZIMH 

Workings

Hint
It doesn't matter how far it was to Manchester, so you can use any distance.

Answer
Billie.

Reasoning
If we call the one way 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, both ways:

   Alex drove 90 + (T − 100)
      = T − 10

   Billie drove (T − 90) + 100
      = T + 10

Therefore, Billie drove 20 miles more than Alex.