Random Puzzles 

Workings

Hint
How far did I travel, and how much fuel did this use?

Answer
I had lost 4 gallons of fuel.

Reasoning
I travelled at 60mph for 4 hours, which is 240 miles.

At 40 miles per gallon this used 6 gallons, which meant the remaining 4 gallons were lost.

Workings

Hint
The answer isn't 9!

Answer
One big one!

Workings

Hint
Going down and across the floor isn't the only route.

Answer
40 feet.

Explanation Diagram
If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.



We can use Pythagoras' theorem (a² + b² = c²) to calculate the distances:
   distance² = horizontal² + vertical²
   distance = √(horizontal² + vertical²)

Route #1
   distance = 1 + 30 + 11 = 42 feet.

Route #2
   horizontal = 6 + 30 + 6 = 42 feet.
   vertical = 10 feet.
   distance = √(42² + 10²) ≈ 43.174 feet.

Route #3
   horizontal = 1 + 30 + 6 = 37 feet.
   vertical = 6 + 11 = 17 feet.
   distance = √(37² + 17²) ≈ 43.178 feet.

Route #4
   horizontal = 1 + 30 + 1 = 32 feet.
   vertical = 6 + 12 + 6 = 24 feet.
   distance = √(32² + 24²) = 40 feet.

Workings

Hint
It doesn't matter what the distance is, so try a random distance.

Answer
This cannot be done.

It does not matter how far the trip is, let's assume that it is random distance, say 60 miles, and remembering that Time = Distance ÷ Speed.

The morning trip took 60 miles ÷ 30 mph = 2 hours.

To average the required 60 mph, we would have to travel the total distance (of 120 miles) in 2 hours. However, we've already used all of the two hours for the morning trip!

Choosing any random distance would also show that it can't be done.