Rate Questions Strategy

[mdecarbo]

I recently took a quant section of a GMAT CAT exam. I came across a few rate questions and wanted to understand the best strategies in tackling them. In general, I have a bit of problem setting these up when it's not straight someone does it at this rate, the other at this rate, what is rate together.. I am going to try to summarize the questions, but I think the idea will get across.

1. Peter does a job alone and it takes 1/x of an hour to complete it. When Adam joins together they get the same job done in an hour. How much of the work does Adam get done in 20 minutes?

2. 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?

Thanks for any input / advice.

[srcc25anu]

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.

[srcc25anu]

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.

[mdecarbo]

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]