SOLUTION: This is a word problem - the problem is - if Janice can paint a room in 10 hours and Jim can paint the same room in 8 hours - how long will it take to paint the room if they both w

Question 33431: This is a word problem - the problem is - if Janice can paint a room in 10 hours and Jim can paint the same room in 8 hours - how long will it take to paint the room if they both work together?
I think the ans should be 4.5 hours but I am not sure how to set up the equation

Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Let t hours be the time to finish the job together.
Janice can finish the job in 10 hours
=> Janice can do t/10 portion of the job in t hours;
Jim can finish the same job in 8 hours
=> Jim can do t/8 portion of the job in t hours.
Total portion of the job done by both Jim and Janice is t hours = 1
=> t/10 + t/8 = 1
=> 4t+5t = 40
=> t = 40/9 = 4 and 4/9 hours
Answer: It will take 4 and 4/9 hours for them to paint the same room together.
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