Most of these answers are hilarious. Anybody who thinks having fewer machines to do the job results in fewer hours to complete the job totally lacks common sense. Imagine a thousand men digging a ditch a kilometer long and it takes them an hour. Will 1 man digging the same trench be finished in less than an hour?
It really is an easy math problem and all you need to do is look at it logically.
If 12 machines do the job in 3 hours, how many hours will it take for only 1 machine?
12 machines = 1 job per 3 hours
In algebraeeze, 12m = 1j / 3h
Multiply both sides by 3h
36mh = 1j
divide both sides by M
36mh / m = 1j /m
36h = 1j/m
Back to English, 36 hours = 1 job per machine.
So if we have 10 machines, we can expect it to take 1 tenth the time that 1 machine would do.
So divide both sides of that equation by 10. That is the same as multiplying both sides by 1/10.
36 h * 1/10 = 1 j/m * 1/10
3.6 h = 1 j / 10m
3.6 hours = 1 job per 10 machines!
Do you wonder why my answer matches dla68?
We are the only ones who showed every step and kept the factors in place. Sure we chose different paths and did things in different sequences, but that is the beauty of math. You can be as creative as you please in your problem solving methodology and as long as you do not violate the basic rules of algebra you will arive at the correct solution.
Comments
Most of these answers are hilarious. Anybody who thinks having fewer machines to do the job results in fewer hours to complete the job totally lacks common sense. Imagine a thousand men digging a ditch a kilometer long and it takes them an hour. Will 1 man digging the same trench be finished in less than an hour?
It really is an easy math problem and all you need to do is look at it logically.
If 12 machines do the job in 3 hours, how many hours will it take for only 1 machine?
12 machines = 1 job per 3 hours
In algebraeeze, 12m = 1j / 3h
Multiply both sides by 3h
36mh = 1j
divide both sides by M
36mh / m = 1j /m
36h = 1j/m
Back to English, 36 hours = 1 job per machine.
So if we have 10 machines, we can expect it to take 1 tenth the time that 1 machine would do.
So divide both sides of that equation by 10. That is the same as multiplying both sides by 1/10.
36 h * 1/10 = 1 j/m * 1/10
3.6 h = 1 j / 10m
3.6 hours = 1 job per 10 machines!
Do you wonder why my answer matches dla68?
We are the only ones who showed every step and kept the factors in place. Sure we chose different paths and did things in different sequences, but that is the beauty of math. You can be as creative as you please in your problem solving methodology and as long as you do not violate the basic rules of algebra you will arive at the correct solution.
1 printing press does the job in 1/4 of an hour, or 15 minutes. 3/12 = 1/4. therefore, 10 presses do the job in 10/4 or 2.5 hours.
think about the situation...you are using less machines...so it will take longer than 3 hours
12 machins has a work rate of 1/3 of a job in 1 hour
so each machine has a work rate of 1/12 of that
so each maching does 1/36 of the job per hour
because 1/3*1/12=1/36
so 10 machings would do 10*1/36 per hour
so 10 machins do 10/36 jobs per hour
x is the # of hours they work
10/36=5/18...to make calculations easire
rate * time = work done
5/18*x=1 (the entire job)
multiply by 18/5
to solve for x
x=18/5
18/5=3.6 hours
.6 hours to minutes = .6*60=36 minutes
so 3 hours 36 minutes
10 presses is two less than you started with.
2/12 = 1/6
1/6 of 3 hours is 1/2 hour.
If you have fewer presses, it should take you longer.
You have 1/6 fewer presses, so 1/6 more time.(?)
that would mean it would take you 3 and 1/2 hours.
3 hours = 6 half hours
12 machines= 6 half hours
2 machines= 1 half hours(doesnt make sense but w/e)
10 machines= 2.5 hours
i think i messed up
2.5 hours
3.6 hours
2.7hr