A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it alone?
Answer: A
Let B do W work in T time. Then A does W/2 work in 3T/4 time. B's rate = W/T. A's rate = (W/2)/(3T/4) = 2W/3T. The ratio of their rates A:B = (2W/3T) : (W/T) = 2/3 : 1 = 2:3. Combined rate is 5 units. Total work = \(5 \times 18 = 90\) units. B's rate is 3 units/day. Time for B alone = 90/3 = 30 days.