How do I solve this question? :

Question

Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours.   Had he done it alone it would have taken Daniel 9 hours.

 

Find how long it would take Paul to do it.

Answer 1

Daniel does 1/9 of the job in one hour

let x= Paul's rate

Paul does 1/x of the job in one hour

together they do the job in 4.95 hours

(1/9)(4.95)+(1/x)(4.95)=1 (job finished)

multiply both sides by 9x

(9x)(1/9)(4.95)+(9x)(1/x)(4.95)=9x(1)

4.95x+9*4.95=9x

4.95x+44.55=9x

9x-4.95x=44.55

4.05x=44.55

405x=4455

x=4455/405

x=11 hours for Paul to do the job alone