Question

Working​ together, Rick and Juanita can complete a job in 6 hr. It would take Rick 9 hr longer than Juanita to do the job alone. How long would it take Juanita​ alone? Round your answer to the nearest​ tenth, if necessary.

Answer 1

Answer:

Juanita Alone will take 9 hours to complete the job.

Solution:

For sake of simplicity let’s assume complete job be represented by W.

Job done by Juanita and Rick together in 6 hours is complete job = W

So job done by Juanita and Rick together in 1 hour = $\frac{W}{6}$

Lets assume number of hours needed by Juanita to complete W work = x hrs

And since Rick takes 9 hours more than Juanita , so number of hours needed by Juanita to complete W work = (x + 9) hrs

Work done by Juanita in 1 hour = $\frac{W}{x}$

Work done by Rick in 1 hour = $\frac{W}{(x + 9)}$

So when they work together, work done in 1 hour = $\frac{W}{x} + \frac{W}{(x + 9)}$

Also initially we evaluated that work done by them in 1 hr = $\frac{W}{6}$

So $\frac{W}{x} + \frac{W}{(x + 9)}$ = $\frac{W}{6}$

$\mathrm{W}\left(\frac{1}{x}+\frac{1}{x+9}\right)=\frac{W}{6}$ = $\frac{W}{6}$

$\frac{1}{x}+\frac{1}{x+9}=\frac{1}{6}$

On cross-multiplication we get

$\frac{(x+9)+x}{x(x+9)}=\frac{1}{6}$

$\frac{2 x+9}{x^{2}+9 x}=\frac{1}{6}$

Again on cross-multiplication we get,

$\begin{array}{c}{12 x+54=x^{2}+9 x} \\ {x^{2}-3 x-54=0}\end{array}$

On splitting the middle term we get

$=x^{2}-9 x+6 x-54=0$

x( x – 9) +6( x – 9 ) = 0

(x+6) (x-9) = 0

When x + 6 = 0, x = -6  

When x – 9 = 0, x = 9

Since x is number of hours, it cannot be negative in given case. So required solution is x = 9.

Hence Juanita Alone will take 9 hours to complete the job.

Answer 2

Answer:

Step-by-step explanation

   this is the equation                                                  r+j=6                      

            this is too                                                         r+9=j      

from the equation you can tell that    r=j-9         if u re=arrange it

now you put     r=j-9     into one of the equation up there   ↑

j-9+j=6

2j=15

j=7.5