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.