There are two inlet pipes to a tank, one taking 8 minutes and the other taking 12 minutes to fill the tank. Find the capacity of the tank if for every second 5 gallons of water is pumped into the tank by the two taps.1) 1600 gallons 2) 1440 gallons 3) 1200 gallons 4) None
Question
There are two inlet pipes to a tank, one taking 8 minutes and the other taking 12 minutes to fill the tank. Find the capacity of the tank if for every second 5 gallons of water is pumped into the tank by the two taps.1) 1600 gallons 2) 1440 gallons 3) 1200 gallons 4) None
Solution
To solve this problem, we first need to find the rate at which each pipe fills the tank.
- The first pipe fills the tank in 8 minutes. Therefore, its rate is 1 tank/8 minutes = 0.125 tanks/minute.
- The second pipe fills the tank in 12 minutes. Therefore, its rate is 1 tank/12 minutes = 0.0833 tanks/minute.
When both pipes are open, they fill the tank at a combined rate of 0.125 tanks/minute + 0.0833 tanks/minute = 0.2083 tanks/minute.
We also know that the combined rate of the two pipes is 5 gallons/second. To convert this to gallons/minute, we multiply by 60 (since there are 60 seconds in a minute), giving us 300 gallons/minute.
Therefore, the capacity of the tank (in gallons) is the combined rate (in tanks/minute) times the conversion factor (in gallons/minute), or 0.2083 tanks/minute * 300 gallons/minute = 62.5 gallons/tank.
So, the capacity of the tank is 62.5 gallons. The answer is 4) None of the above.
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