Random Puzzles 

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

Workings

Hint
The first letters of the words are: D, D, F, I, L, L, P, S, S, S.

Answers
dif + fer + ent = different
dig + est + ive = digestive
far + mho + use = farmhouse
imp + ort + ant = important
lib + rar + ian = librarian
lig + htn + ing = lightning
por + tfo + lio = portfolio
sca + rec + row = scarecrow
sin + cer + ely = sincerely
som + eth + ing = something

Workings

Hint
Both words begin with the letter B.

Answer
Brainy and binary.

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