thoh13 wrote:/PAINTERS 2/
Mark and Try want to paint a wall - the same wall. Mark wants it to be taupe but Try wants it to be mauve. Mark can paint the wall by himself in one hour but Try takes two hours (sorry Try). Try, knowing he can't win, wants to make Mark's job as hard as possible. So they start painting at the same time. Try even paints over Mark's taupe with his mauve (which Mark will have to repaint). Within what range of times will the wall be completely toupe?
markr wrote:PAINTERS 2
If Try is smart, he can make it take two hours. If he's dumb, Mark can still finish in one hour.
smart: he only paints over Mark's work
dumb: he only paints where Mark hasn't painted
My answer:
In the worst case scenario, Mark and Try start painting from the same corner. Mark paints the wall taupe in one hour, but by that time, Try has painted over half of Mark's paint with mauve. Now Mark has an extra half a wall to paint in half an hour, at which point Try adds 1/4th of a wall to repaint again. Then 1/8th, 1/16th, and so on. The wall gets painted taupe in 1 + 1/2 + 1/4 + 1/8 + ... = 2hrs.
In the best case scenario, Mark and Try start painting from opposite corners. In 40 minutes (2/3 hr) they meet, when Mark has painted 2/3rds of the wall taupe and Try painted 1/3rd mauve. Now Mark has to paint 1/3rd of the wall, but Try starts painting on Mark's taupe (since he's been credited with not mindlessly repainting his own mauve). This adds 1/6th of the wall for Mark, and later 1/12th, and so on. The wall gets painted taupe in 2/3 + 1/3 + 1/6 + 1/12 + ... = 1 1/3 hrs or 1 hr 20 min.
So the wall will be paited between 1 hr 20 min and 2 hrs.
