SOLUTION: If Sara can paint a house in 4 hours and Bill can paint the same house in 6 hours how long will it take them to paint the house together?? What is the formula for figuring this

Question 299860: If Sara can paint a house in 4 hours and Bill can paint the same house in 6 hours how long will it take them to paint the house together??
What is the formula for figuring this out and why?
Answer by sharon1948(6) (Show Source): You can put this solution on YOUR website!
The forumla is:
Rate x Time = total work done

Let "t" = total time to paint together
Sara = 4 hrs
Bill = 6 hrs
1 (job)/4 hrs x t + 1 (job)/6 hr x t= total time worked together
1 x t = t
t/4 + t/6 = total time worked together
You have to find a comman denominator when adding fractions
t/4 x 6/6 + t/6 x 4/4 = 6t/24 + 4t/24 = 10t/24
10t=24
divide both sides by 10
t = 2.4 hrs or 2 2/5 hrs do to the job together

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