It seems that our first lesson was too difficult for most of you uneducated ducklings. I've scaled back the difficulty of today's lesson in the hope of receiving acceptable responses from more of you. Let's hope this works; if it doesn't then I don't know what I am going to do.

Kisume was in a pickle. When dropping down to scare the passing shrine maiden, she accidentally dropped too far. Her bucket hit the ground and broke. Now she needs a new bucket. Unfortunately Rinnosuke's shop is out of buckets, and Kisume doesn't have any spares readily available. Thus she must make a new bucket from scratch. Our friendly shrine maiden was enchanted by Kisume's pathetic cuteness and has offered to help.

Kisume's bucket is primarily made of wood. Unfortunately, all of the wood from her last bucket splintered into unusable shards upon impact. However, all other components of her previous bucket are reusable. Reimu and Kisume will need to gather up wood to build a new bucket with.

Kisume, as a young child, has difficulty gathering wood. However, she is industrious and able to work without interruption. She can gather 16 cubic inches of wood per hour.

Reimu has no trouble gathering wood. She can gather 32 cubic inches of wood per hour if she works uninterrupted. However, it seems that Reimu is unable to escape interruption no matter where she goes. If she tries to gather wood at her shrine then there is a 43% chance of being pulled into drunken reveling at her hot springs with every citizen in Gensokyo. This will reduce her wood gathering effectiveness by 78%. However, if she tries to gather wood anywhere else then there is a 99% chance that she will have to take a break to save Gensokyo from a heretofore unknown youkai who is trying to eliminate the clouds so that Gensokyo will become a sunnier place. While doing this she would only be able to gather wood at a rate of sqrt(graze/573) cubic inches per hour.

Luckily for Kisume, she has bucket building directions handy that dictate how much wood is needed and how long building the bucket will take once all the material is gathered together. The directions are reproduced here:

1) How long will it take Kisume and Reimu to gather the materials for and build Kisume's bucket? Assume that Reimu rationally decides upon the optimal wood gathering option available to her.

2) Now consider the case when friendly Yamame has witnessed the accident. She wants to help her bucketloli friend out, but is unable to effectively gather wood on her own. Instead she accompanies Reimu on her wood gathering trips, chasing off interruptions with threats to give them swine flu. This reduces Reimu's chance of interruption in all cases by 23%. Furthermore, Yamame is a skilled craftswoman and will speed up the actual building process by 5% per f she adds to the total noise level of construction. How fast can the Yamame-Reimu-Kisume trio gather the wood and build the bucket?

Don't let me down class. Be sure to take time to think about your answer before you begin writing,