anonymous one year ago Quick algebra question?

1. anonymous

Hi I need help solving this problem – Andrew can paint the neighbor’s house 6 times as fast as bailey. The year Andrew and Bailey worked together, it took them 5 days. How long would it take each ti paint the house? Andrew__ days? Bailey ____ days? The way I set up problem:

2. anonymous

$\frac{ 5 }{ x }+\frac{ 5 }{ 6x }=1$

3. anonymous

4. anonymous

@Mikuxluka can you help?

5. jim_thompson5910

You have the correct equation. The next step I would do is multiply both sides by the LCD 6x to clear out the fractions

6. anonymous

x=5?

7. jim_thompson5910

$\Large \frac{ 5 }{ x }+\frac{ 5 }{ 6x }=1$ $\Large {\color{red}{6x}}*\left(\frac{ 5 }{ x }+\frac{ 5 }{ 6x }\right)={\color{red}{6x}}*1$ $\Large {\color{red}{6x}}*\frac{ 5 }{ x }+{\color{red}{6x}}*\frac{ 5 }{ 6x }={\color{red}{6x}}*1$ $\Large {\color{red}{6\cancel{x}}}*\frac{ 5 }{ \cancel{x} }+{\color{red}{\cancel{6x}}}*\frac{ 5 }{ \cancel{6x} }={\color{red}{6x}}*1$ $\Large 6*5 + 5=6x$ Let me know if this enough to get going

8. jim_thompson5910

x = 5 is incorrect

9. anonymous

wouldnt it be 6*5+5=6x 35=6x x=5?

10. jim_thompson5910

35 = 6x does not lead to x = 5

11. jim_thompson5910

you're probably thinking 30 = 6x

12. anonymous

oops lol so x=35/6 . so that would be the first answer..how would I find Baileys time?

13. jim_thompson5910

x = 35/6 is correct now compute 6x by replacing x with 35/6

14. anonymous

I am sorry I dont understand that :(

15. jim_thompson5910

|dw:1441070231979:dw|

16. jim_thompson5910

multiply both sides by 6 to go from "x" on the left side to "6x" |dw:1441070258679:dw|

17. jim_thompson5910

|dw:1441070271344:dw|

18. jim_thompson5910

so in a way, we already had the value of 6x when we were trying to isolate x earlier

19. anonymous

Ok I see that. So 35/6 days would be Andrews answer. How would I find Baileys?

20. jim_thompson5910

x = 35/6 6x = 35 Andrew takes 35/6 = 5.833 (roughly) days while Bailey takes 35 days (since 6x represents Bailey's time)

21. anonymous

Oh wow now I see it. thanks so much for ur help have a great night!

22. jim_thompson5910

you're welcome