If Person A Can Paint A Hall In 5 Hrs And Person B Can Paint The Same Hall In 9 Hrs What Is Their Rate Working Together

If person A can paint a hall in 5 hrs and person B can paint the same hall in 9 hrs, what is their rate working together?

Solution

The answer is (1/5) + (1/9) = 14/45, that is the hall will be painted in 3 3/14 hrs.   Now why you say???   A’s rate is “hall”/5 hrs AND b’s rate is “hall”/9 hrs.  If they work together for T hours, then they will accomplish T * “hall”/5 hrs + T * “hall”/9 hrs and that should be equal to the rate working together for hrs = T “hall”/ x hrs Now you see that the T and “hall” both divide out and you are left with   (1/5) + (1/9) = 1/x which is what I started with.