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 to paint the elephant. How long would it take Curly to paint the elephant if he worked alone?

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 to paint the elephant. How long would it take Curly to paint the elephant if he worked alone?

Thanks.

Answer 1

Larry paints L elephants/minute

Moe paints M elephants per minute
Curley paints C elephants per minute

(L + M + C )(3) = 1 elephant
(L) (10) = 1 elephant
(M)(6) = 1 elephant
so
L = 1/10
M = 1/6
(1/10 + 1/6 + C )(3) = 1
3/30 + 5/30 + C = 10/30
C = 2/30 = 1/15 elephants per minute
so
15 minutes per elephant

Answer 2

To determine how long it would take Curly to paint the elephant if he worked alone, we can start by assigning rates of work to each person. Let's say the rate of work for Larry is L (in elephants per minute), for Moe is M (in elephants per minute), and for Curly is C (in elephants per minute).

Given that Larry, Moe, and Curly can paint an elephant together in 3 minutes, we can express their combined rate of work as:
1/3 = L + M + C (equation 1)

We also have the information that:
Larry can paint an elephant alone in 10 minutes, so his individual rate of work is 1/10: L = 1/10 (equation 2)
Moe can paint an elephant alone in 6 minutes, so his individual rate of work is 1/6: M = 1/6 (equation 3)

Now, to find Curly's individual rate of work (C), we substitute equations 2 and 3 into equation 1:
1/3 = 1/10 + 1/6 + C

To add the fractions on the right side, we need a common denominator of 30:
1/3 = 3/30 + 5/30 + C
1/3 = 8/30 + C

Now, rearranging the equation to solve for C:
C = 1/3 - 8/30
C = 10/30 - 8/30
C = 2/30
C = 1/15

So, Curly's individual rate of work is 1/15 elephants per minute. Since it takes one rate unit to paint one elephant, it would take Curly 15 minutes to paint the elephant if he worked alone.