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
A little algebra might help.

Answer
I have 14 apples, and you have 28 apples.

Reasoning
We can work this out with a little algebra. I have A apples, and you have B apples, then
[1]  5 x (A − 7) = B + 7

[2]        A + 7 = B − 7

From [1] we have:

    5A − 35 = B + 7
[3]      5A = B + 42

From [2] we have:

[4]  A + 14 = B

We can then use [4] in [3] to give:

  5A = (A + 14) + 42
  5A = A + 56
  4A = 56
   A = 14

Which gives B = 28 (by [4]).

Workings

Hint
Does the answer change = NO.

Answer
 

Workings

Hints
The first letters of the words are: B, P, S, D, A, T, D, C, W, G.

Answers
---jos = banjos ---icy = policy ---uld = should ---bts = doubts ---nda = agenda ---phy = trophy ---may = dismay ---ese = cheese ---mth = warmth ---axy = galaxy