The situation that you have considered in not Logical. Peter completes a job in 1/x hrs. and Peter + Adam complete it in 1 hour. This is not logical since when Adam joins in, the work should get completed sooner than later and 1/x < 1. If x = 2, we are saying Peter alone can complete a job in 1/2 hour but when Adam also joins him, they complete in 1 hour.

usually the problem is of the form that it takes X hours for A to complete the job. and A+B can complete it in Y hours where Y < X.

So lets say Peter can complete a job in 6 hours and when Peter and Adam work together, they can finish the job in 4 hours. what is Adam's rate of work (OR how much work can Adam alone complete in 20 mins = 1/3rd of an hour)

Let us assume total work = some mult. of 6 and 4
let say TOTAL WORK = 12
In 1 hour:
Peter can do 12/6 = 2 units of work
Peter + Adam can do 12/4 = 3 units of work
Therefore Adam must be doing 1 unit in 1 hour

Now if Adam does 1 unit in 1 hour, he must be doing 1/3 units in 1/3 hour.

Q2. Machine A does a job in a certain time, Machine B does the same job in a certain time. When doing the job together, how much of the work does Machine B NOT have to complete?

Let Mach A complete a job in 3 hours
Let Mach B complete a job in 5 hours
if they work together, the rate of work that Mach A does to rate of work that Mach B does will be in the ratio of their respective speeds

So we need to know the speed of work for both Mach A and Mach B.
Lets consider some multiple of 3 and 5 as total work to be done.
Let W (total Work) = 15
In 1 hour:
Mach A does 15/3 = 5 units/hr
mach B does 15/5 = 3 units/hr
What % of work Mach B NOT have to complete or simultaneously what % of work does Mach A HAVE to complete.
That will be 5*100/8 % or 62.5%

Another approach:
Ratio of Time in INVERSELY PROPORTIONAL to ratio of speeds
if TIME of MAch A: TIME of MAch B = 3:5
Thus Speed of MAch A: Speed of MAch B = 5:3
How much work B HAVE to complete: 3/8
How much work B NOT HAVE to complete? 1-3/8 = 5/8 (which is equal to Mach A speed of work)
as speed and work done are directly proportional. Faster the speed, more work completed.

Sorry,

I think that I asked the question wrong.

Peter can do 1/x of the job in an hour[/b]... that might make the question logical.[/b]