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katen-ka-za [31]
3 years ago
10

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.
Mathematics
2 answers:
Valentin [98]3 years ago
8 0

<u>Answer:</u>

Juanita Alone will take 9 hours to complete the job.

<u> Solution: </u>

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.

Gekata [30.6K]3 years ago
4 0

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

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