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
How many boxes of toys can 1 toy maker make in 5 hours?

Answer
Five toy makers.

Reasoning
How many boxes of toys can 1 toy maker make in 5 hours?
2 toy makers can make 6 boxes of toys in 3 hours
1 toy maker  can make 3 boxes of toys in 3 hours
1 toy maker  can make 1 box   of toys in 1 hour
1 toy maker  can make 5 boxes of toys in 5 hours

So 4 toy makers could only make 20 boxes of toy in 5 hours, and we require the extra toy maker to make the remaining 2 boxes of toys.

Workings

Hint
The first letters of the words are: B, A, S, A, B, B, R, N, B, C.

Answer
BINARY = BRAINY
ABROAD = ABOARD
RASCAL = SCALAR
ALTARS = ASTRAL
BADGER = BARGED
BARKED = BRAKED
MARBLE = RAMBLE
UNABLE = NEBULA
TABLET = BATTLE
CALLER = CELLAR or RECALL

There are some less common anagrams such as:
RASCAL = SACRAL
ALTARS = TARSAL
ALTARS = RATALS
ALTARS = TALARS
BADGER = GARBED
BARKED = DEBARK
MARBLE = BLAMER
MARBLE = AMBLER
MARBLE = LAMBER
UNABLE = UNBALE
TABLET = BATTEL

So you can have an extra half point if you found one of these! There are some even rarer anagrams, but I don't think I'll allow those!

Workings

Hint
How many large pipes are required to drain the reservoir in 24 hours?

Answer
21 hours and 36 minutes.

Reasoning
Looking at the first clue:
   in 12 hours, 6 large pipes can drain 1 reservoir
   in 24 hours, 6 large pipes can drain 2 reservoirs
   (*) in 24 hours, 3 large pipes can drain 1 reservoir

Looking at the second clue:
   in 8 hours, 3 large + 9 small pipes can drain 1 reservoir
   in 24 hours, 3 large + 9 small pipes can drain 3 reservoirs

But, by (*), we know that in those 24 hours, 3 large pipes can drain 1 of those reservoirs.

Therefore, the other 2 reservoirs can be drained by the small pipes on their own:
   in 24 hours, 9 small pipes can drain 2 reservoirs
   in 24 hours, 1 small pipe can drain ²/₉ reservoirs
multiply the hours by 9:
   in 216 hours, 1 small pipe can drain 2 reservoirs
   in 216 hours, 5 small pipes can drain 10 reservoirs
divide the hours by 10:
   in 21.6 hours, 5 small pipes can drain 1 reservoir

21.6 hours = 21 hours and 36 minutes.