12th grade
posted by diane .
it takes bill 4 hours to paint a house. it takes john 7 hours to paint the same house. how long does it take to paint the house if they painted it together.

If you put the name of the subject then the correct teacher can give you help more quickly.

Area of the house to be painted = A
Bill pains "B" area per hour
John pains "J" area per hour
So, A/B = 4 hours, and A/J = 7 hours
=> B = A/4 and J = a/7
B and J says how much area they can paint per hour.
When both of them work together, assume it takes x hours to finish the work
=> xB + xJ = A the total area painted
x(A+B) = x(A/4+A/7)=A
x (1/4+1/7)= 1 so x = 28/11 
Jacob's answer explains it better, but there is an equation you can use.
Tt = 1/T1 + 1/T2
where Tt is total time, T1 is the first person's time, and T2 is the second person's time (this can be carried out as far as needed, such as by adding a 1/T3 term, and a 1/T4 term, etc.). 
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