Hints and solutions to Draw a Picture #4

One painter can paint a wall in ten minutes. Another painter can paint it in 6 minutes. About how long will it take both painters to do the job if they work together? (Assume they don't get in each other's way!)

• The hint given with the problem said to think about how much of the wall each painter could paint in one minute, so let's do that first.
• Since the first painter takes ten minutes to paint the whole wall, he paints 1/10 of the wall each minute.
• Since the second painter takes six minutes to paint the whole wall, he paints 1/6 of the wall each minute.
• So we can draw a picture of what gets done in one minute if they work together:
  

  The yellow part is the part of the wall that gets done in one minute. You can see that, working together, the two painters can paint 1/6 + 1/10 = 4/15 of the wall in one minute.

• Since they paint 4/15 of the wall in one minute, it will take them 15/4 minutes (or 3 minutes and 45 seconds) to finish the whole wall.