# SOLUTION: A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it ta

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 Question 149574: A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job?Answer by ankor@dixie-net.com(15622)   (Show Source): You can put this solution on YOUR website!A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job? ; Let a = time required when A works alone Let b = time required when B works alone : Let the completed job = 1 : write an equation for each scenario : "A and B working together can do a job in 24 hours." + = 1 Multiply equation by ab to get rid of the denominators, results 24b + 24a = ab 24a = ab - 24b 24a = b(a-24) = b : "After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. That means a worked 27 hrs + = 1 Multiply equation by ab to get rid of the denominators, results 27b + 20a = ab 20a = ab - 27b 20a = b(a-27) = b : Therefore: = Cross multiply: 24a(a-27) = 20a(a-24) : 24a^2 - 648a = 20a^2 - 480a : 24a^2 - 20a^2 -648a + 480a = 0 : 4a^2 - 168a = 0 : 4a(a - 42) = 0 : a = +42 A's hrs alone ; Use + = 1 to find b, substitute 42 for a + = 1 Multiply equation by 42b 24b + 42(24) = 42b : 1008 = 42b - 24b : 1008 = 18b b = b = 56 hrs is B's time alone ; : You can check solution using a calc on both equations, a=42, b=56