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Workings

Answer
Illegible, eggshells and bobsleigh. The longest word is bibliologies with 12 letters.

Workings

Hint
Try removing the Y from ENERGY.

Answers
energy    -y = green oregano   -o = orange clearest  -e = scarlet weight    -g = white outlive   -u = violet embark    -k = amber calmer    -l = cream or -r = camel solemn    -s = lemon voiding   -v = indigo archery   -a = cherry

Workings

Hint
How many rooms can Alex clear in 36 hours?

Answer
12 hours.

Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.

So, 2 + 2 − 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.

Alternative Reasoning
Alex and Billie can each empty ¹/₁₈ of the bookshelves in 1 hour, but Drew will refill ¹/₃₆ of the bookshelves in one hour.

So in one hour we have ¹/₁₈ + ¹/₁₈ − ¹/₃₆ = ¹/₁₂.

So it would take 12 hours to empty the bookshelves.

Workings

Hint
The question is written in English, but not in its usual order.

Answer
32.

Reading one letter from the top row and then one from the bottom row, the puzzle reads: 'How many letters does this puzzle have'.