HOW LONG WOULD IT TAKE MACHINE b TO DO THE JOB BY ITSELF

Question

copying machines A and B, working together, can prepare enough copies of the annual report for the board of directors in 2 hours. Machine A, working alone, would require 3 hours to do the job. How long would it take machine B to do the job by itself

Answer 1

The work rate for machine A is 1/3 of the whole job per hour.

Assume the work rate for machine B is 1/b i.e. b is the time in hours for B to do the whole job by itself (except for a person to load it up and push appropriate buttons).

 

The whole job done by both machines in 2 hours translates into this equation:   1 = (1/3)(2) + (1/b)(2)

 

1 - 2/3 = 2/b                    1/3 = 2/b.       This is a proportion (two fractions equated).  One of the nice properties of a proportion is that you can take reciprocals, so 3/1 = b/2, i.e. half of b = 3  so b = 6.

 

It takes machine B 6 hours, working 'alone.'