3. Professor Ma has a stack of 40 essays to grade. By herself, the professor can grade about five essays in two hours. Her teaching assistant, Chen, can grade about seven essays in three hours. About how many hours (1) would it take both of them to grade all 40 essays if they work together?

We can set up fractions to represent how much each one of them can grade in one hour. To do this, divide the number of essays by the number of hours it would take for them to grade them. Therefore, the professor would be able to grade 5/2 essays in one hour, and her assistant would be able to grade 7/3 essays in one hour.

Now, set up your equation.

5/2x + 7/3x = 40

Since x = number of hours spent grading, multiply that by the respective fractions we calculated earlier to get the number of essays they would grade in x hours. Set the equation equal to 40 as you are looking for 40 essays done.

Now, solve the equation. First, set a common denominator, add the two fractions together, then simplify.

5/2x + 7/3x = 40

15/6x + 14/6x = 40

29/6x = 40

x = 40/(29/6)

x = 40 * (6/29)

x = 240/29

x = about 8.3

Therefore, your answer is about 8.3 hours, or about 8 - 9 hours.

Hope this helps!