Medium Puzzles 

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.

Workings

Hints
The first letters of the words are: P, B, D, L, O, A, B, H, S, B.

Answers
pro + nou + nce = pronounce
bea + uti + ful = beautiful
dim + ens + ion = dimension
liv + est + ock = livestock
ope + rat + ion = operation
ann + oun + cer = announcer
bed + spr + ead = bedspread
hou + seb + oat = houseboat
sev + ent + een = seventeen
bre + akf + ast = breakfast

Workings

Hint
The answer isn't a whole number of years, and algebra might be required.

Answer
29 years 2 months.

Reasoning #1
This answer is taken directly from the original book.

The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.

Reasoning #2
Here's my answer, with a little algebra.

If we call Tommy T, Mamma M and Papa P we can see that:

"our three ages add up to exactly seventy years" gives us:

(1)   T + M + P = 70

"Just six times as old as you" gives us:

(2)   P = 6 x T

In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:

(3)   P + Y = 2 x (T + Y)

and "our three ages will add up to exactly twice as much as today" gives us:

   (T + Y) + (M + Y) + (P + Y) = 140

which can be written as

(4)   T + M + P + 3Y = 140

We can see from (4) and (1) that

     3Y = 70

so

(5)   Y = 70 ÷ 3

Using (2) and (5) in (3) we have

            P + Y = 2 x (T + Y)

   6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)

            4 x T = 70 ÷ 3

(6)             T = 70 ÷ 12

We can now use (6) in (2) to see that:

   P = 6 x T

   P = 6 x 70 ÷ 12

   P = 70 ÷ 2

And using the values for T and P in (1) we have:

              T + M + P = 70

   70 ÷ 12 + M + 70 ÷ 2 = 70

Multiply throughout by 12 to give:

   70 + 12 x M + 420 = 840

              12 x M = 840 − 420 − 70

              12 x M = 350

                   M = 350 ÷ 12

So:

   Tommy = 70 ÷ 12   = 5.83333  = 5 years 10 months.
   Papa  = 70 ÷ 2    = 35       = 35 years.
   Mamma = 350 ÷ 12  = 29.1666  = 29 years 2 months.

Workings

Hint
The words are linked by their letters.

Answer
Approved.

The initial letters spell ORANGE and the last letters spell INDIGO.