Question

Josephine can correct her students’ test papers in 5 hours, but if her teacher’s assistant helps, it would take them 3 hours. How long would it take the assistant to do it alone?

Answer 1

To find out how long it would take the assistant to correct the test papers alone, we can use the information given in the question.
Let's assume that the number of test papers to be corrected is the same in both cases.
If Josephine can correct the test papers alone in 5 hours, then she can correct 1/5 of the test papers in one hour.
If Josephine and her assistant can correct the test papers together in 3 hours, then they can correct 1/3 of the test papers in one hour.
Let's assume that the assistant can correct 1/x of the test papers in one hour.
Then, we can set up the following equation:
1/5 + 1/x = 1/3
Multiplying both sides by 15x, we get:
3x + 15 = 5x
2x = 15
x = 7.5
Therefore, the assistant can correct the test papers alone in 7.5 hours.

Answer 2

Explanation:

1 job divided by the sum of the rates = 3 hours

1 / ( 1/5 + 1/x ) = 3

x = 7.5 hrs for assistant alone