water from a tank is being used for irrigation while the tank is being filled. The two pipes can fill the tank in 6h and 8h, respectively. the outlet pipe can empty the tank in 24h. How long would it take to fill the tank with all three pipes open? round the answer to the nearest decimal plce.
4 hours
how much of the tank is filled each hour?
1/x = 1/6 + 1/8 - 1/24
1/x = 1/4
x = 4 hours
To find out how long it would take to fill the tank with all three pipes open, we need to calculate their combined filling rates.
Let's denote the filling rates of the two inlet pipes as R1 and R2, and the draining rate of the outlet pipe as R3.
We know that the time it takes to fill the tank is inversely proportional to the filling rate. So, we can represent this relationship mathematically as:
Time = Volume / Rate
Since the volume of the tank does not affect the calculation (it cancels out), we can assume a volume of 1 unit for simplicity.
Given that the first inlet pipe fills the tank in 6 hours, its filling rate can be calculated as 1/6 units per hour (1 volume unit filled over 6 hours).
Similarly, the second inlet pipe fills the tank in 8 hours, so its filling rate is 1/8 units per hour (1 volume unit filled over 8 hours).
The outlet pipe empties the tank in 24 hours, so its draining rate is 1/24 units per hour (1 volume unit emptied over 24 hours).
To find the combined filling rate of all three pipes, we need to add the filling rates of the inlet pipes and subtract the draining rate of the outlet pipe:
Combined filling rate = R1 + R2 - R3
So, substituting the values:
Combined filling rate = (1/6) + (1/8) - (1/24) = 4/24 + 3/24 - 1/24 = 6/24 = 1/4 units per hour.
Now, we can calculate the time it takes to fill the tank with all three pipes open:
Time = 1 unit / Combined filling rate = 1 / (1/4) = 4 hours.
Therefore, it would take approximately 4 hours to fill the tank with all three pipes open.