## Grazes 3 years ago A worker can build a fence in 8 hours, With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?

1. Lily_980

Wouldn't it be the same amount of hours?

2. JamesWolf

What was wrong with my previous answer?

3. JamesWolf

9 hours.

4. Grazes

Not necessarily. And could you please show some work?

5. JamesWolf

well lets say the assistant worked at the same rate as the worker. then it would take half the time, 4 hours right.

6. Grazes

Oh. Nevermind. The answer is 40/3 hours.

7. JamesWolf

oh :(

8. JamesWolf

13 hours? how?

9. Grazes

Worker=W Assistant=A 1/A+1/W=1/5 1/A+1/8=1/5 8+A/8A=1/5 5*(8+A)=8A 40+5A=8A 3A=40 A=40/3 hours

10. JamesWolf

are you sure?

11. JamesWolf

why 1/A ?

12. Grazes

It's the work rate.

13. Grazes

Algebra.

14. JamesWolf

why is the rate 1/A ?

15. JamesWolf

sorry, i dont get it

16. Grazes

So it takes you 6 minutes to shower, right?

17. Grazes

You've showered for 2 minutes already. Doesn't that mean that you showered for 2/6 of the regular shower time or 1/3?

18. Grazes
19. JamesWolf

That makes sense.