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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.

Workings

Hint
In the road race, where could Charlie have finished?

Answer
Cycling : Billie > Alex > Charlie > Drew

Road race : Drew > Charlie > Billie > Alex

Road Race
In the road race, where could Charlie have finished?

By (4), he wasn't last. By (5), he wasn't first.

By (2), if Charlie was third, then he would have won the cycling, but by (3) Alex beat Charlie in the cycling, so Charlie can't have won the cycling.

So Charlie must have finished in second place.

By (5), Drew was first.

By (1), Alex didn't win the cycling, so by (2) he didn't come third in the road race. Therefore, Alex came last.

Leaving Billie in third place.

Road race : Drew > Charlie > Billie > Alex

Cycling
By (2), Billie won.

By (4), Charlie wasn't last.

By (3), Alex beat Charlie. So Alex finished in second place, with Charlie in third place.

Leaving Drew in last place.

Cycling : Billie > Alex > Charlie > Drew

Workings

Hint
One of the words end in K. Remember that a skunk isn't a reptile, or an amphibian.

Answers
-r-g       = frog -o-t-i-e   = tortoise -n-k-      = snake -e-t       = newt -i-a-d     = lizard -r-c-d-l-  = crocodile -a-a-a-d-r = salamander -u-t-e     = turtle -k-n-      = skink a-l-g-t-r  = alligator

Workings

Hint
A 3-letter word becomes a 4-letter word.

Answer
Red.

Reasoning
red + a = read.