The ratio of the time taken by A and B to complete a task is 3 : 2. If B can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?
10.8 hours
Step 1 – find A's time:
If A : B = 3 : 2 in time and B alone = 18 h, then A alone = \(18 \times \dfrac{3}{2} = 27\) hours.
Step 2 – combined rate:
\(\dfrac{1}{27} + \dfrac{1}{18} = \dfrac{2 + 3}{54} = \dfrac{5}{54}\)
Step 3 – time together:
\(T = \dfrac{54}{5} = 10.8\ \text{hours}\)
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