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.

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 =

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 =

Work done by Rick in 1 hour =

So when they work together, work done in 1 hour =

Also initially we evaluated that work done by them in 1 hr =

So =

=

On cross-multiplication we get

Again on cross-multiplication we get,

On splitting the middle term we get

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.

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step-by-step explanation:

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