Hint: How long did it take for Peter to reach the waterfall?
Answer: 20 miles.
The dog always ran at twice Peter's speed. Since Peter ran 10 miles the dog ran 20 miles.
A local farmer wants to keep his horses safe.
He has one mile of fence, with which to surround the horses.
Luckily there is a very straight river which he can also use.
Obviously the farmer wants to fence off as much land as possible, what shape will the fenced off area be and how large?
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Hint: You might need to remember the formula for the area of a circle (= Pi x radius x radius)
The fenced off area will be a large semicircle, with the river forming the diameter of the circle and the area will be 0.16 of a square mile.
As the fence forms the curved semicircle section, so half the circle has a length around of 1 mile (the fence), so the whole circle has a circumference of 2 miles. As circumference = Pi x diameter, then diameter = circumference / Pi. In this case the diameter is therefore 2 / Pi and the radius is therefore 1 / Pi.
The area of the entire circle would be Pi x (1 / Pi) x (1 / Pi) = 1 / Pi.
We only want half of this area, so the answer is 1 / (2 x Pi) = 0.16 of a square mile.
Note: if the farmer were to make a square area (using the river as one side), each side would be 1/3 of a mile, and 1/3 x 1/3 = 0.11 of a square mile, which is smaller.
A rich aristocrat decided that he would give every man 45 dollars and every woman 60 dollars.
Only one ninth of the men and only one twelfth of the women collected their dues.
Can you tell me how much money the aristocrat spent if there were 3552 people in total?
Hint: Tops of thermometers can't be filled unless the bottoms are.