Answer: it will take the assistant to do it alone 17 1/2 hours
Step-by-step explanation:
Let x represent the number of hours it will take the assistant to do it alone. This means that the unit work rate per hour is 1/x
If Josephine can correct her students’ test papers in 7 hours, it means that the unit work rate per hour is 1/7
If both of them can do the job in 5 hours, it means that their combined unit rate is 1/5
Since the rates are independent, it means that
1/x + 1/7 = 1/5
The lowest common multiple of the denominators is 35x. Multiplying through by 35x, we have
35 + 5x = 7x
7x - 5x = 35
2x = 35
x = 35/2 = 17/2
it will take the assistant to do it alone 17 1/2 hours