Word Problems: Work Problems Questions~?

Question

I need help getting to the answer of this question.

Mr. R , a college instructor, can grade his class papers in 3 hours while it takes his assistant 4 1/2 hours. If Mr. R graded the papers for 1 hour and then left the job for his assistant to complete, how long will it take his assistant to finish grading papers?
Answer = 1/3 hours

This is what i did and i still can't get the answer
1/3 + (1/4.5)x = 1

Answer 1

[06]
Mr R can complete the jon in 3 hrs
Therefore in 1 hour he completes 1/3 part of the job
Remaiing work
=1 -1/3=2/3 part
his assistant can do the job in 4 1/2 or 9/2 hrs
Therefore in 1 hr he can do 2/9 part of the job
Hence for finishing remaining 2/3 pat of the job,he would take
2/3 divided by 2/9
=2/3*9/2
=3 hrs
Please note that the answer given is incorrect

Answer 2

The answer is not 1/3 hr. The answer is 3 hrs.

In one hour, Mr R grades 1/3 of the papers. That leaves 2/3 of the papers for the assistant.

Since the assistant can grade them all in 4.5 hr, he can grade 2/3 of them in 4.5 * 2/3 = 3 hrs.

If the back of your book says 1/3, it's wrong.

Answer 3

Since it normally takes 3 hours and he only spent 1, he graded 1/3 of his papers which leaves 2/3 for his assistant.

so 4.5/1=x/(2/3)
x=4.5*2/3
x=9/3
x=3 hours

Answer 4

1/3 per hour = speed of Mr. R, 1/(4 1/2) per hour = speed of his assistant

= (1 - 1/3) / (1 / [4 1/2])
= 2/3 / (1 / [9/2])
= 2/3 / (1 * 2/9)
= (2/3) / (2/9)
= 2/3 * 9/2
= 18/6 or 3

Answer: 3 hours

Proof:
= (1 hr * 1/3 per hour) + (3 hr * [1 job / {4 1/2 per hour}])
= 1/3 job + (3 hr * [1 job / {9/2 per hour}])
= 1/3 job + (3 hr * [ 1 job * 2/9])
= 1/3 job + (3 hr * 2/9)
= 1/3 job + 2/3 job
= 1 job