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A group of workers in a puppet manufacturing company was assigned the task of making 395 puppets. Each worker in the group works at a constant rate and makes five puppets per hour. At the end of the first hour, some of the workers were assigned to another task; at the end of the second hour, the same number of remaining workers were also reassigned to another task, and a similar reassignment occurred at the end of every hour till the task was complete. If the entire task was completed in 4 hours and 20 minutes, how many puppets were finished in the first three hours?
Let initial number of workers be 'a', and number of workers assigned to another tasks be 'd'.
From the statement we can form the equation
5*{a +(a-d) + (a-2d) + (a-3d) + (a-4d)*(20/60)}= 395
simplify the equation to get
13a = 237 + 22d
Now, substitute values of d from 1, we find at d=4 a= 25, at higher values of d the term (a-4d) will become negative.
reqd answer is 5*(a + (a-d) + (a-2d)); [substitute a=25 and d=4 here]
answer = 315
