an inlet pipe can fill a large water tank in 3 hours. an outlet pipe can empty the same tank in 5 hours. given an empty tank, at 8pm, activate both pipes. what time on the clock will it be before the tank is completely filled?
In any given hour,
fraction of tank filled, x = 1/3-1/5 = 2/15
Time to fill = 1/x = 15/2 = 7.5 hours
To find out at what time the tank will be completely filled, we need to determine the rate of filling and emptying the tank in terms of volume per hour.
Let's denote the volume of the tank as V, which is the quantity that needs to be filled.
The inlet pipe fills the tank in 3 hours, so the rate of filling is V/3 per hour.
The outlet pipe empties the tank in 5 hours, so the rate of emptying is V/5 per hour.
When both pipes are active simultaneously, the net rate at which the tank is being filled (inflow minus outflow) is:
(V/3) - (V/5) = (5V - 3V) / 15 = 2V / 15
This means that the tank is being filled at a rate of 2V / 15 per hour.
Since we know that the tank is initially empty and needs to be completely filled, the time required to fill the tank is given by:
Time = Volume / Rate
Plugging in the values, we get:
Time = V / (2V / 15) = 15 / 2
Therefore, the tank will be completely filled after 15/2 hours, which is equivalent to 7.5 hours.
Starting at 8 pm, if we add 7.5 hours to the time, we get:
8 pm + 7.5 hours = 3:30 am
So, the tank will be completely filled at 3:30 am.