Today is the first day of July's Problem of the Week. Rather than giving a thorough explanation of each problem, I will just give a hint. The hint may be the formulas you need or something to help you achieve the answer.

Remember to write down the answer you receive after each day so that you can plug it in for the next day's problem.

Easy: Normally, I begin the week with triangles, but I thought that I would change it up this time and start with a puzzle.

If a goose and a half can lay an egg and a half in a day and a half, then how many eggs e can a half a gross of geese lay in a half a day?

e =

Hint: a gross is a dozen dozens.

Hard: Again, I am not starting the week with triangles, but a puzzle instead. This puzzle is much harder.

You are stuck out in the wilderness and the only thing that you can possibly eat that is anywhere near you is a plant. The plant is poisonous, but it takes exactly 15 minutes over a flame to kill the poison. However, it takes exactly 15 minutes over the flame to activate another poison in the plant. So, if you cook it for exactly 15 minutes, it is safe to eat, but just a little more or a little less and you will die from the poison.

You don't have any timers, watches, phones, or clocks. All you have is two ropes that take exactly an hour to burn when the end is lit. However, it may not burn equally all the way through (a quarter of the rope probably won't burn in exactly 15 minutes).

Using just these two ropes and the fire, you can cook the plant for exactly 15 minutes. Once you figure out how (which is the hard part), tell me how long it will take to actually get your food.

t =

Hint: first, figure out the problem if the plant took exactly 30 minutes to become harmless.

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