Word Problem for "WORK" (constant-rate machines)

[mcheytan]

Each of 10 machines works at constant rate to do a job. The 10 machines together can accomplish the work in 16 hours. How many hours are needed for only 8 machines to complete the same job.

I figured: Each of the 10 machines is doing 1/16 of the job in 1 hour. There are 10 machines total=10/16 for the 10 machines working for ONE hour.
In the second case, we have only 8 machines and we have X to be the total time they need to complete the job. THerefore 8/X is the per hour productivity of 8 machines.

Then what I need to do to get the x? The answer is 20 hours...and I cant get it
Please help

 

[Mrspi]

Re: Word Problem for "WORK"

Each of 10 machines works at constant rate to do a job. The 10 machines together can accomplish the work in 16 hours. How many hours are needed for only 8 machines to complete the same job.

I figured: Each of the 10 machines is doing 1/16 of the job in 1 hour. There are 10 machines total=10/16 for the 10 machines working for ONE hour.
In the second case, we have only 8 machines and we have X to be the total time they need to complete the job. THerefore 8/X is the per hour productivity of 8 machines.

Then what I need to do to get the x? The answer is 20 hours...and I cant get it
Please help

If 10 machines complete the job in 16 hours, it must take 10*16 machine-hours to do the job.

It will take 160 machine-hours to do the job, regardless of the number of machines used. For example, if we let x = number of hours required for 5 machines to do the job, it must be true that 5 machines * x hours = 160 machine-hours, or 5x = 160. This would give us 32 hours for 5 machines.

Can you apply this approach to your problem?

 

[mcheytan]

Re: Word Problem for "WORK"

Thanksss!!!! I totally did not think about the 160 before!!!he-he-he!I got it!