Question

Three​ painters, beth,​ bill, and​ edie, working​ together, can paint the exterior of a home in 1212 hours. bill and edie together have painted a similar house in 1515 hours. one​ day, all three worked on this same kind of house for 1010 ​hours, after which edie left. beth and bill required 55 more hours to finish. assuming no gain or loss in​ efficiency, how long should it take each person to complete such a job​ alone?

Answer 1

Let be be Beth, bi be Bill, and e be edie. Then:
1/be + 1/bi +1/e=1/12
1/bi + 1/e=1/15
10/be +10/bi +10/e+5/be+5/bi=1
Solve for be, bi, and e
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