task/day
You write the problem in the form of task per day per machine. Then you multiply by the number of machines. So you have one task. As written if it takes six machines to complete one task in two days. Then it would take 12 machines to complete the same task in one day. So you have reduced the problem a bit. Is that how you would do it? If you solve for the number of days. 4 machines are what fraction of 12? The difficulty of written problems is to reduce the words to abstract numerical form so you can easily apply the known equations. But you have to start with writing down separate equations and reducing a factor to unity (1). So you start with 1 task equals 6 machines. 6 machines equal 2 days. Now what do you want to solve for? You need to know how many of what? The answer is to say that: 1 task equals 6 machines equals 2 days. So 6 machines equals 2 days/task. Then you can solve for either days or machines and then do the multiplication. It is necessary to write down in mathematical notation the known conditions. If you learn to do that simple task, the rest is easy.
CBS
Good explanation!
However, when teaching kids math, you have to write down each step and number the steps as you along.
Also be sure to SPACE the numbered steps.
T is the time required for 1 machine to complete the task
1/T+1/T+1/T+1/T+1/T+1/T=1/2
6/T=1/2 or T=12
one machine takes 12 days to complete the task.
Time required for 4 machines is
1/12+1/12+1/12+1/12=4/12=1/3
so 4 machines takes 3 days to complete the task.
The question becomes more messy if there are 5, 7, or 11 machines as 5,7&11 are mutually prime with 12
12 is divisible by 2,3,4,6 and 8,9,10 have common factors with 12, but the same processes still work in determining time to task completion.
Rap
