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Workings

Hint
How much petrol was used for the journey itself?

Answer
3 gallons each hour.

Reasoning
I drove 300 miles at 30 miles per gallon, so I used 10 gallons. Which means I lost the other 15 gallons.

I drove the 300 miles at 60mph, which took me 5 hours.

So I lost 15 gallons of petrol in 5 hours = 3 gallons per hour.

Workings

Hint
The word starts with the letter D.

Answer
Difficult.

Workings

Hint
A little algebra might help.

Answer
¹/₈.

Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 − 3) x 4 − n = 20

Expanding the brackets and simplifying gives:

(2n^2 + 8 − 3) x 4 − n = 20

    (2n^2 + 5) x 4 − n = 20

         8n^2 + 20 − n = 20

              8n^2 − n = 0 (*)

                8n − 1 = 0

                    8n = 1

                     n = ¹/₈

In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.

Double-Checking
                 ¹/₈
   squared     = ¹/₆₄
   add 4       = 4¹/₆₄
   double      = 8¹/₃₂
   take away 3 = 5¹/₃₂
   times 4     = 20¹/₈

   subtracting ¹/₈ gives 20, as required.

Workings

Hint
The bottom word begins with P.

Answer