Step 1:
In order to solve this problem, first find out Zack's work rate indicated as 1/Z (1 house in Z hours).
According to the question, the total work rate of all three people together is 1/2 (1 house in 2 hours), Ann's work rate is 1/5 (1 house in 5 hours), and Matt's work rate is 1/6 (1 house in 6 hours).
Each person contributes his share to that total rate, meaning:
Ann + Matt + Zack = total
1/5 + 1/6 + 1/Z = 1/2
=> 1/Z = 1/2 – 1/5 – 1/6 //30 is the lowest common denominator
=> 1/Z = (15-6-5)/30 //Multiply both sides by 30
=> 30/Z = 15 – 6 – 5
=> 30/Z = 4 //*Z
=> 30 = 4Z //Divide both sides by 4
=> Z = 7.5
Thus, Zack's work rate: 1/7.5
Step 2:
The total time it will take both Ann and Zack to clean a house:
1/t = 1/5 + 1/7.5 //15 is the lowest common denominator
=> 1/t = (3+2)/15
=> 1/t = 5/15
=> 1/t = 1/3 // Multiply both sides by 3t
=> t = 3 hours.