Nolan B. answered • 07/12/23
Incoming Class of 2027 UGA Math Major with a Passion for Teaching
First we must find the rate that the original 12 glassblowers made each singular vase. We can think this logically without math for a moment and deduce that 12 glassblowers each made 1 vase during those 9 minutes as their numbers were identical. Sidenote: If the number of vases created was not equal to glassblowers we would divide the number of vases by glassblowers to approximate the amount each singular glassblower contributed towards the number of vases. In other words, how many vases were made per glassblower if you want to think about it in a word sense rather then formulaic (vases/glassblowers). Since we know that 1 glassblower contributed to 1 vase in a 9 minute period, we can divide 1 glassblower by 9 minutes to obtain how many vases one glassblower contributes towards making a vase per minute. Once this answer is found (I will refer to this answer as Y, since it will be easier for typing/reading) we must multiply this by 8 for the new problem, and this will provide the productivity of 8 glassblowers in an 1 minute period. Y * 8 will give us a new answer of 8/9 (which I'll refer to as X). To find the final answer we must divide X by 32 as this will provide us how many minutes it will take 8 glassblowers to produce the 32 vases. This will do this by showing us the number of groups of X it will take to reach the number 32 (each group is 1 minute, and don't get too confused by this extra sentence as I'm just explaining the simplicity of division to build understanding of why we divide these numbers in the manner that we do here). Answer: 36 minutes
