Re: If 6 typists, all working at the same rate, can complete a document in
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30 Jul 2020, 23:29
Generalise understanding
Our objective is to generalise our understanding as much as we can, so we deal with one concept that can be applied to multiple situations with a slight change in terminology. This problem is of the type x people/machines work for y hours to do certain work. That x could be typists, painters, tree planters, machines, labourers, etc.
Approach
When 6 people/machines work for 4 hours, visualise it in your mind. 6 people sewing clothes for 4 hours. 6 painters painting a house for 4 hours. 6 machines running in a factory and producing biscuits. Now what does that mean? Simplify further. 6 people sewing clothes for 4 hours means each of them has worked for 4 hours, since they all were sitting in the factory and working for the entire 4 hours. So the total number of hours of work done is 6 x 4 = 24 hours of work done. Pause for a while. Understand what this means. This means that we got 24 hours of work done. So now we can express work done not in terms of number of shirts produced but in terms of no of hours. So if we had to get 48 hours worth of work done, those 6 people would have to sit for twice the amount of time - 8 hours, which is 48/6. Generalise this in your mind. I first need to know the total amount of work that needs to be done in terms of hours, and then divide that by the number of people who are working.
In the present case, if 6 typists worked for 4 hours and got the document done, how much total typing would they have done? All the 6 were sitting in that room and each typist typed for 4 hours. So they together typed for 24 hours in total - hence our work to be done is equivalent to 24 hours worth of work. Now if the same work needs to be done by only 4 typists, they would need 24/4 = 6 hours. Looking at it from their perspective, if only 4 typists were available, either 1 would have to work for 24 hours (because the work is such that it takes 24 hours), or 2 could work for 12 hours each (you type half the document while I type the other half), or 3 could work for 8 hours each, or all the 4 could work for 6 hours each.
Conclusion
When x people/machines work together for y hours, each of them works for y hours each, so the total work done is worth xy hours. If the no. of people/machines decrease, the same work would need more time to complete, since everyone is working with the same efficiency or rate.