Question

A high school mathematics teacher can grade a set of exams in 5 hours working alone. If their student teacher helps them, it will take them 3 hours to grade the exams together. How long would it take the student to grade them exams if they worked alone?

Type your answer rounded to two decimal places below
It would take the student teacher ___ hours to grade alone.​

Answer 1

To find out how long it would take the student teacher to grade the exams alone, their rate is combined with the teacher's rate when working together. Solving the equation for the student teacher's rate reveals it would take them 7.50 hours to grade alone.

Step-by-step explanation:

To calculate how long it would take the student teacher to grade the exams alone, the rate at which both the teacher and the student teacher work together and separately must be determined. Since the teacher can grade the exams in 5 hours, their rate is 1 set/5 hours. Let's denote the time it takes the student teacher to grade the exams alone as t hours, so their rate would be 1 set/t hours.

When they work together, their combined rate is 1 set/3 hours. By adding the individual rates, we get:

1/5 + 1/t = 1/3

To find the value of t, we solve the equation:

1/t = 1/3 - 1/5

1/t = 5/15 - 3/15

1/t = 2/15

t = 15/2

t = 7.5 hours

Therefore, it would take the student teacher 7.50 hours to grade the exams alone, rounded to two decimal places.

Answer 2

7 hours

Step-by-step explanation:

Well, i'm not entirely sure about the answer, but if the high school teacher can do it in 5 hours and if the teacher does it with the student teacher in 3 hours (2 hours less) then instead of subtracting add 2 hours to the student teacher which would be a total of 7 hours.