If 6 typists, all working at the same rate, can complete a document in

In order to solve this problem we need to need to know the work rate of one typist; because all the typists work at the same rate we can imagine a series that must reduce to 1 job / 4hours. In this problem, the game Challenge 24 can be particularly helpful as a supplementary cool down from QA studying or warm up ( and I don't mean this facetiously but rather to as a way to maintain interest and improve one's mental math). If we imagine 1 machines completes in x amount of hours then the sum of 6 machines completes 6 jobs in x amount of hours. For this problem, perhaps because of early exposure to Challenge 24, it just popped it in my 6 fractions must add up to fraction with 6 in the numerator ( the amount of jobs completed) divided by denominator that allows the fraction to be reduced to 1 job in 4 hours. If six machines working at a constant rate of 1 job /24 hours combine their work rate then 6 jobs are completed in 24 hours, or 6 jobs / 24 hours. This reduced to 1 job in 4 hours or 1 job / hours. Now that we know the work rate, we just add 1/24 four times or really the numerator times 4 and reduced- 1 job- 6 hours.

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.