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A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?


8 hours

12 hours

24 hours

Verified Answer :

12 hours..........
+ - = 1
Multiply by 12 to clear the fractions
3t + 2t - 4t = 12
t = 12 hrs to fill the pool

Answer:

12 hours

Step-by-step explanation:

Let t be time to fill with all pipes open

All the pipes will complete a single job that is = 1

Given is that the tank can be filled by one pipe in 4 hours and by a second pipe in 6 hours and can be drained by a third pipe in 3 hours.

So, equation forms;

\(\frac{t}{4}+ \frac{t}{6}- \frac{t}{3}=1\)

=> \(\frac{3t+2t-4t}{12} =1\)

=> \(\frac{t}{12} =1\)

And t = 12 hours

Hence, it will take 12 hours to do the job.

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