Random Puzzles 

Workings

Hint
Adding the speeds won't work.

Answer
205 mph.

Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.

The first ²/₅ are covered at 123 mph. Therefore, the time taken was [(²/₅) x L] ÷ 123 hours.

The next ²/₅ are covered at 164 mph. Therefore, the time taken was [(²/₅) x L] ÷ 164 hours.

The last ¹/₅ is covered at y mph. Therefore, the time taken was [(¹/₅) x L] ÷ y hours.

The entire trip is covered at an average of 150 mph, and we can conclude that:
 2L      2L      L     L
————— + ————— + ——— = ———
5x123   5x164    5y   150

Rearranging and simplifying gives:
 1     1    2     2
——— = —— - ——— - ———
 y    30   123   164

That means that y = 1 ÷ (¹/₃₀ − ²/₁₂₃ − ²/₁₆₄)

Using a calculator gives y = 205.

Workings

Answer
1680.

This is n to the power of 5, starting with 2^5 = 32, with the last digit missing, 7^5 = 16807.

Workings

Hint
Is there a missing letter?

Answer
Attempts.

This word contains the only letter E in the entire paragraph, notice how every other letter appears at least once.

Although the letters C, E, J, Q, V, X each all appear once, the longer the piece of text the more difficult it is to avoid the letter E.

Workings

Hint
Each line adds to 14.

Answer