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

Hint
Try working backwards.

Answer
Saturday.

Reasoning
It's best to work backwards:

   "Sunday's tomorrow"

is Monday.

   "the day after Sunday's tomorrow"

is therefore Tuesday.

   "five days before the day after Sunday's tomorrow"

is therefore Thursday.

   "yesterday was five days before the day after Sunday's tomorrow"

yesterday was Thursday, making today Friday. Therefore, tomorrow is Saturday.

Workings

Hint
A little algebra might help.

Answer
He will be 35 in 14 years.

Reasoning
He is currently 21.

If X is his current age, then:
  X = 14 +  X
           ———
            3
so

   2X = 14
  ———
   3

and

  2X = 42

So

  X = 21

He is currently 21 and his favourite book is currently 14 years old, when it is 28 years old (double its age) he will be 35.

Workings

Hint
There are fewer than 20 squares.

Answer
18 squares.

In the solution below, you can see 6 squares in the middle, with another 12 squares around the outside.