1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Paint Can Problem

  1. Sep 7, 2008 #1
    There are two 1-gallon (4 quarts) cans. One contains 4qt of white paint, and
    the other contains 3qt of red paint. You pour 1 qt of white paint into the red, mix it, and then pour 1 qt of the mixture back into the can of white paint. What is the
    red-white content of each can now? If you continually repeat
    the process, when will the two cans be the same shade of pink?
     
  2. jcsd
  3. Sep 8, 2008 #2
    You start out with white-to-red ratios of:
    Can 1: 4:0
    Can 2: 0:3

    After 1qt of Can 1 is added to Can 2:
    Can 1: 3:0
    Can 2: 1:3

    After 1 qt of Can 2 is added to Can 1:
    Can 1: 3.25:0.75
    Can 2: 0.75:2.25

    Do this process 10 times total, and you get approximately:
    Can 1: 2.291150649:1.708849351 ~ 1.340756
    Can 2: 1.708849351:1.291150649 ~ 1.323509

    Do it 20 times and you get approximately:
    Can 1: 2.285731526:1.714268474 ~ 1.333356799
    Can 2: 1.714268474:1.285731526 ~ 1.333302047

    So, you slowly get closer and closer to the ultimate:
    Can 1: 16/7 white paint, 12/7 red paint = 4:3 ratio
    Can 2: 12/7 white paint, 9/7 red paint = 4:3 ratio

    But you never quite get there, mathematically speaking.

    DaveE
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Paint Can Problem
  1. Painting mystery (Replies: 6)

  2. Michelangelo's Paint (Replies: 5)

  3. Painting job (Replies: 2)

  4. Paint job (Replies: 13)

Loading...