Question

Students make a big mess in the cafeteria at lunch. 9 students had 30 minutes to clean up the mess.They got mad and named 3 others that were guilty. The principal added their names to the clean up crew and changed the time limit. How much time should she give them to complete the job?

Answer 1

22.5 minutes

Explanation:

Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.

After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.

Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:

9 · 30 = 12 · t

Solving for "t":

270 = 12t

t = 270 / 12

t = 22.5

So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.