Random Puzzles 

Workings

Hint
The word begins with the letter T.

Answer
Tattooists.

Which has 10 letters.

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45

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
For example, E7 would be England.

Answers
H5 = Haiti V9 = Venezuela D7 = Denmark J7 = Jamaica F6 = France N6 = Norway P4 = Peru Z8 = Zimbabwe R7 = Romania Q5 = Qatar