Two pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all three pipes are opened together, then the time taken to fill the tank is:
Two pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all three pipes are opened together, then the time taken to fill the tank is:
Solution
Pipe A fills the tank in 5 hours, so in 1 hour it fills of the tank.
Pipe B fills the tank in 6 hours, so in 1 hour it fills of the tank.
Pipe C empties the tank in 12 hours, so in 1 hour it empties of the tank.
When all three pipes are opened together, the combined work in 1 hour is:
The LCM of 5, 6, and 12 is 60.
Converting each fraction:
Combined rate
Combined rate of tank per hour
If of the tank is filled in 1 hour, then the time to fill the complete tank is:
Time
Time
Time hours
Converting to mixed fraction:
with remainder
hours
Therefore, the time taken to fill the tank is hours.
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