pattydread wrote:

Could someone help me on this work question:

6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

The answer is 3 but I don't understand how it was derived.

Thanks folks

I crack such qs this way--You need to understand the logic behind the working though.

6 macs, 1 job, 12 days -----> 1 day, 6 macs, 1/12th of the job OR mathematically, 6m==1/12 (where m is the rate of job completion each machine)

6m=1/12

m=1/(12*6) (Remember, in the denominator, 12 represents the job completion days and 6 represents the number of machines) --> (i)

m=1/72 (that is, each machine can complete 1/72th of the job every day; it is the rate of a machine)

Now, break up the denominator to have job completion days and number of machines. refer (i) for the format

m=1/72=1/(8*9)

Why 8*9? we need 8 in place of 12 i.e. we need some n number of machines to work for us and complete the same job in 8 days instead of 12 days. We can afford to have such a break up because the machines are still the same: rates won't change.

so, 8 represents the number of days and 9 represents the number of machines.

9m=1/8 OR verbally, 9 machines are required to complete a job in 8 days.

Hope this helps!

_________________

Is this okay?