Question

Professor Dorsey is grading papers in the teachers' lounge. She has already finished grading 21 assignments, and is grading 2 more assignments per hour. Her teaching assistant just came in to help her. She can grade at a rate of 9 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How many assignments will they each have graded? How long will that take?

Professor Dorsey and her assistant both will have graded ___ assignments in
___hours.

HELPPP

Answer 1

Let's start by setting up an equation to represent the situation. Let "x" be the number of hours they work together, and "y" be the number of assignments they each grade. We know that Professor Dorsey has already graded 21 assignments, and is grading 2 more assignments per hour. Her assistant can grade 9 assignments every hour. So, the equation is:

21 + 2x = 9x + y

Simplifying this equation, we get:

y = 7x + 21

Since they will have graded the same number of papers, we can set their number of assignments equal to each other:

7x + 21 = 9x

2x = 21

x = 10.5

So, they will work together for 10.5 hours. To find the number of assignments they each graded, we can substitute the value of "x" into the equation we derived earlier:

y = 7x + 21
y = 7(10.5) + 21
y = 73.5

Therefore, Professor Dorsey and her assistant will each have graded 73.5 assignments in 10.5 hours. However, since they cannot grade a fraction of an assignment, we can round down to the nearest whole number. So, they will each have graded 73 assignments in 10.5 hours.