Twelve typists, all working with the same speed, type a certain number of pages in 18 days, working 8 hrs a day. find how many hours per day must sixteen typists work in order to type the same number of pages in 18 days
We know that working 8 hours per day for 18 days results in 144 days.
Since we are increasing the number of typists by 16/12 or 4/3 the number of hours they work per day must be inversely proportional. So we know that if there are 12 typists we need 4/3 times more hours than if we have 16 typists. Therefore we have to multiply by the number of hours that it takes 12 typists by 3/4 to solve.
144 * 3/4 = 108
Now we know it takes 108 hours in total, and that means that 108/18 hours or 6 hours per day.
6 hours per day! :)
Also, note that instead of converting the number of hours per day to the total amount of hours, since the number of days they are working constant, we could've just kept it constant and ignore the number of hours they are working per day, so then it will be 8 * 3/4 which gives us 6 hours as previously predicted.