SOLUTION: if someone takes hours to paint a room, and another person takes 12 hours to paint a room, if the two of them work together at the same pace, how long would it take them?

Question 356834: if someone takes hours to paint a room, and another person takes 12 hours to paint a room, if the two of them work together at the same pace, how long would it take them?
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
if someone takes hours to paint a room, and another person takes 12 hours to paint a room, if the two of them work together at the same pace, how long would it take them?

person A --> ? hours to fill a room, did you forget to say how many hours?, well lets call that A hours then since the number is not here
person B --> 12 hours to paint a room
how long would it take them to paint the room working together?

total time T hours = (1 job)/[(1 job)/(A hours) + (1 job)/(12 hours)]
hours = jobs/(jobs/hours) = jobs * hours/jobs = hours (that is the units)
T = 1/(1/A + 1/12)
T = 1/(12/12A + A/12A) (multiplied 1/A by 12/12 and 1/12 by A/A)
T = 1/((12 + A)/12A)
T = 12A/(12 + A) hours
if we know A, we can find T

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