Question

working together, Larry, Moe, and Curly can paint an elephant in 3 minutes. Working alone it would take Larry 10 minutes or Moe 6 minutes. How long will it take for Curly to paint the elephant alone

Answer 1

I'm only answering this one because I like the Three Stooges.

What's important in these questions is the rates, work per unit time, add up when we have multiple people.

Let c be Curly's rate in elephants per minute. Larry's rate is 1/10 elephants per minutes and Moe's is 1/6 elephants per minute. For the three of them to get done in three minutes means their collective rate is 1/3 elephants per minute:

`1/3 = 1/10 + 1/6 + c`

`c = -1/10 - 1/6 + 1/3 = -3/30 - 5/30 + 10/30 = 2/30 = \frac 1 {15}`

Curly's rate is 1/15 th of an element per minute, so it would take him 15 minutes to paint an elephant.