Random Puzzles 

Workings

Hint
How much of a warren can each rabbit dig in one hour?

Answer
2 hours.

Reasoning
The small rabbit can dig a warren in nine hours, so digs ¹/₉ in one hour.

The medium rabbit can dig a warren in 6 hours, so digs ¹/₆ in one hour.

The large rabbit can dig a warren in four and a half hours, so digs ¹/_4.5 in one hour.

   1 Hour = ¹/₉ + ¹/₆ + ¹/_4.5

To make the denominators all the same, we can multiply through by ¹⁸/₁₈ to give:

   1 Hour = ²/₁₈ + ³/₁₈ + ⁴/₁₈

   1 Hour = ⁹/₁₈

   1 Hour = ¹/₂

So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.

Workings

Hint
One of the words is waterfall (wat + erf + all).

Answers
som + eth + ing = something
hai + rbr + ush = hairbrush
gra + ssl + and = grassland
pin + eap + ple = pineapple
pol + ice + man = policeman
mea + nwh + ile = meanwhile
wat + erf + all = waterfall
sca + rec + row = scarecrow
yes + ter + day = yesterday
obs + tin + ate = obstinate

Workings

Hint
The first word starts with H.

Answer
Hard and soft.

Workings

Hint
The first nine prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23.

Answer
29.

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.