Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:
Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:
Solution
The tank's capacity is liters.
Pipe 1 fills the tank in 6 minutes, so in 1 minute it fills liters.
Pipe 2 fills the tank in 12 minutes, so in 1 minute it fills liters.
Pipe 3 empties at 18 liters per minute.
All pipes together fill the empty tank in 5 minutes, so in 1 minute they fill liters.
In 1 minute, the net filling rate is:
The LCM of 6, 12, and 5 is 60.
Multiplying the entire equation by 60:
The capacity of the tank is 360 litres.
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