SOLUTION: Jack accepted a job to paint a new house. He calculated that he can complete the job in 30 hours. He hired a trainee to assist him. He has seen the trainee work and estimates that

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Question 266025: Jack accepted a job to paint a new house. He calculated that he can complete the job in 30 hours. He hired a trainee to assist him. He has seen the trainee work and estimates that it the trainee working alone would take 45 hours to complete the job. How much time should the two of them working together need to paint the house? (Round your answer to the nearest tenth.)
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time needed to paint the house when both are working together
Then together they paint at the rate of 1/x house per hour
Jack paints at the rate of 1/30 house per hour
Trainee paints at the rate of 1/45 house per hour
Together they pain at the rate of 1/30 + 1/45 house per hour
So, our equation to solve is:
1/30 + 1/45=1/x multiply each term by 90x
3x+2x=90
5x=90
x=18 hours----------------------------time needed when both are working togeether
CK
(1/30)*18 + (1/45)*18 needs to equal 1
54/90 + 36/90=1
1=1
Hope this helps---ptaylor