If they worked alone, how long would each of the workers take to finish the work?

Question

Two workers were given some work. When the first one had worked for 7 hours and the other worker for 4 hours, It turned out, that in total they had done 5/9 of total work. Now

they worked together for another 4 hours and the work remained to be done after that was

18/1.

Sorry for my English. I hope you can understand my question.

Answer 1

I believe you mean 1/18 at the end. Letting R be rate of 7 hour worker and r the rate of the 4 hour worker, you have the simultaneous equations:

7R + 4r = 5/9 and 4R + 4r = 1-5/9-1/18 = 7/18

If you subtract the equations as they are you get 3R = 5/9 - 7/18 so you can find R in fractions of Job/hour and use either equation to solve for r.