# SOLUTION: .A and B can do a piece of work in 12 days,B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each take to complete the job?

Algebra ->  Algebra  -> Rate-of-work-word-problems -> SOLUTION: .A and B can do a piece of work in 12 days,B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each take to complete the job?      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Word Problems: Rate of work, PAINTING, Pool Filling Solvers Lessons Answers archive Quiz In Depth

 Question 268391: .A and B can do a piece of work in 12 days,B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each take to complete the job?Answer by ankor@dixie-net.com(15622)   (Show Source): You can put this solution on YOUR website!Let the piece of work = 1 : Write a shared work equation for each phrase: : A and B can do a piece of work in 12 days, + = 1 : B and C can do it in 15 days and + = 1 ; C and A can do the same work in 20 days. + = 1 : Use elimination; Mult the 1st eq by 5, mult the 3nd eq by 3 + = 5 + = 3 ------------------------------Subtraction eliminates A, leaving us with - = 2 : Multiply the 2nd equation by 4, add to the above equation - = 2 + = 4 -------------------------------addition eliminates C, find B = 6 120 = 6B B = B = 20 hrs working alone : Use the 2nd equation to find C, substitute 20 for B, find C + = 1 Multiply by 20C, results: 15C + 20(15) = 20C 15C + 300 = 20C 300 = 20C - 15C 5C = 300 C = C = 60 hrs working alone : Use the 3rd equation to find A + = 1 Multiply by 60A 60(20) + 20A = 60A 1200 = 60A - 20A 40A = 1200 A = A = 30 hrs working alone : Summarize: A=30; B=20; C=60 ; : Check it in the 1st equation + = 1 + = + = 1 : YOu can confirm it in the other two equations.