Random Puzzles 

Workings

Hint
Look at the second letter in each word.

Answer
Guava.

The second letter of the words are the vowels (AEIOU) in order.

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10

Workings

Hint
This is a very common sequence.

Answer
N, T.

Nine, ten!

Workings

Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.

Answer
119mph.

Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.

Using:
   Time = Distance ÷ Speed

The first two laps took:
   ¹⁰/₁₀₀ hours

The second two laps took:
   ¹⁰/₁₀₂ hours

The next two laps took:
   ¹⁰/₁₄₀ hours

The final two laps took:
   ¹⁰/₁₅₀ hours

Therefore, the total time for the 8 laps was:
   ¹⁰/₁₀₀ + ¹⁰/₁₀₂ + ¹⁰/₁₄₀ + ¹⁰/₁₅₀ hours
   = ¹/₁₀ + ⁵/₅₁ + ¹/₁₄ + ¹/₁₅ hours

Looking at the denominators:
   10 = 2 x 5
   51 = 3 x 17
   14 = 2 x 7
   15 = 3 x 5

The lowest common multiple (LCM) of these numbers is 2 x 3 x 5 x 7 x 17 = 3570.

   = ³⁵⁷/₃₅₇₀ + ³⁵⁰/₃₅₇₀ + ²⁵⁵/₃₅₇₀ + ²³⁸/₃₅₇₀ hours
   = ¹²⁰⁰/₃₅₇₀ hours
   = ¹²⁰/₃₅₇ hours
   = ⁴⁰/₁₁₉ hours

The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
   average speed = 40 ÷ (⁴⁰/₁₁₉)
   average speed = 40 x (¹¹⁹/₄₀)
                 = 119 mph