A tank is filled with an intake pipe that will fill it in 5 hours and an outlet pipe that will empty it in 15 hours. If both pipes are left open, how long will it take to fill the empty tank?
1/5 - 1/15 = 1/x
2/15 = 1/x
x = 15/2
To find out how long it will take to fill the empty tank, we need to determine the combined rate at which the intake pipe and outlet pipe fill or empty the tank. Let's first determine the rate at which each pipe fills or empties the tank.
The intake pipe fills the tank in 5 hours. Therefore, in 1 hour, it fills 1/5th of the tank.
The outlet pipe empties the tank in 15 hours. So, in 1 hour, it empties 1/15th of the tank.
Now, let's calculate the combined rate at which both pipes fill or empty the tank when they are left open together. To do this, we can find the difference between the rates of the intake and outlet pipes.
Combined rate = Rate of intake - Rate of outlet
= 1/5 - 1/15 (taking the positive value as we are interested in filling the tank)
Simplifying the above expression, we get:
Combined rate = 3/15 - 1/15
= 2/15
This means that when both pipes are open, the tank is being filled at a rate of 2/15th per hour.
To calculate how long it will take to fill the empty tank, we can use the formula:
Time = Tank capacity / Combined rate
Since we want to fill the empty tank completely, the tank capacity is 1 (assuming it is a unit tank).
Time = 1 / (2/15)
= 15/2
= 7.5 hours
Therefore, it will take 7.5 hours to fill the empty tank if both the intake and outlet pipes are left open.