Solve the word problem.

Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?

Ron

a0 days

Lee

a1 days

Ron: 6+2√5 days ≈ 10.47 days

Lee: 2+2√5 days ≈ 6.47 days

Step-by-step explanation:

Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...

1/L + 1 / (L+4) = 1/4

Multiplying by the product of denominators, we get ...

4 (L+4) + 4L = L (L+4)

Subtracting the left side gives ...

L^2 - 4L - 16 = 0

Completing the square, we can write this as ...

L^2 - 4L + 4 = 20

(L - 2) ^2 = 20

L = 2 + √20 = 2 + 2√5 ≈ 6.47

Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.

Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.