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Pipes A and B fill a tank in 12 and 16 hours. B is opened 2 hours after A. Counting from when A was opened, how long does the tank take to fill?

Competition practicePipes & Cisterns

A $6 \frac{6}{7} h$
B8 h
C $8 \frac{6}{7} h$
D $7 \frac{5}{7} h$

Step-by-Step Solution

If the time is

t : \frac{t}{12} + \frac{t - 2}{16} = 1 \Rightarrow 4 t + 3 t - 6 = 48 \Rightarrow t = \frac{54}{7} = 7 \frac{5}{7}

h

. (6 \frac{6}{7}

h is the time if both started together.)

Answer: D)

7 \frac{5}{7} h

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