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 daysLee a1 days
Accepted Solution
A:
Answer: Ron: 6+2√5 days ≈ 10.47 days Lee: 2+2√5 days ≈ 6.47 daysStep-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) = 1/4Multiplying by the product of denominators, we get ... 4(L+4) +4L = L(L+4)Subtracting the left side gives ... L^2 -4L -16 = 0Completing the square, we can write this as ... L^2 -4L +4 = 20 (L -2)^2 = 20 L = 2 + √20 = 2 +2√5 ≈ 6.47Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.