if sally can paint a house in 4 hours, and john can paint the same house in 6 hours how long will it take both of them to paint the same house together. Let the answer be x hours: >>...sally can paint a house in 4 hours...<< So in one hour she can paint 1/4th of a house So in x hours she can paint x times 1/4th of a house, or x/4ths of a house >>...john can paint the same house in 6 hours...<< So in one hour he can paint 1/6 of a house So in x hours he can paint x times 1/6th of a house, or x/6ths of a house Therefore the x/4ths of a house that Sally paints plus the x/6ths of a house that John paints must equal 1 house painted, so x/4 + x/6 = 1 Solve that by multiplying thru all terms by LCD of 12 Answer = 2.4 hours or 2 hours 24 minutes. Edwin