Random Puzzles 

Workings

Hint
Look at the letters more closely.

Answer
Michael.

Each name begins with the last letter of the preceding name.

Workings

Hint
The first word begins with T.

Answer
Too many cooks spoil the broth.

Reasoning
The saying has been broken down into blocks of 4, the last block has been filled with dummy letters. Each block has then been reversed.

Double-Checking
Start with:
   TOO MANY COOKS SPOIL THE BROTH

Group together:
   TOOMANYCOOKSSPOILTHEBROTH

Split into groups of 4 letters:
   TOOM ANYC OOKS SPOI LTHE BROT H

Add 3 random characters:
   TOOM ANYC OOKS SPOI LTHE BROT HBCY

Reverse each group of 4 letters:
   MOOT CYNA SKOO IOPS EHTL TORB YCBH

Workings

Hint
Break down 210 into its factors.

Answer
12357.

Reasoning
Since 210 = 2 x 3 x 5 x 7, 12357 is the only way to get a 5-digit number, in ascending order.

Workings

Hint
It doesn't matter what the distance is, so try a random distance.

Answer
This cannot be done.

It does not matter how far the trip is, let's assume that it is random distance, say 60 miles, and remembering that Time = Distance ÷ Speed.

The morning trip took 60 miles ÷ 30 mph = 2 hours.

To average the required 60 mph, we would have to travel the total distance (of 120 miles) in 2 hours. However, we've already used all of the two hours for the morning trip!

Choosing any random distance would also show that it can't be done.