A tank is filled in 9 hours and drained in 11 hours. How long will it take to fill the tank if the drain is left half open
Find out what percentage of the tank is filled every hour, and then calculate how long it would take to reach 100%.
To find out how long it will take to fill the tank if the drain is left half open, we first need to calculate the rates of filling and draining the tank.
Let's assume that the tank has a capacity of 1 unit (for simplicity).
The rate at which the tank is filled is 1 unit per 9 hours, and the rate at which it is drained is 1 unit per 11 hours.
To determine the combined rate of filling and draining, we subtract the draining rate from the filling rate:
Rate of filling and draining = Rate of filling - Rate of draining
Rate of filling = 1 unit / 9 hours
Rate of draining = 1 unit / 11 hours
Rate of filling and draining = (1/9) - (1/11)
To find the time it takes to fill the tank when the draining is left half open, we divide the tank's capacity by the combined rate of filling and draining:
Time to fill the tank = Capacity / (Rate of filling and draining)
Since we assumed the capacity of the tank as 1 unit:
Time to fill the tank = 1 / [(1/9) - (1/11)]
Now, let's calculate the time it takes:
Time to fill the tank = 1 / [(11/99) - (9/99)]
= 1 / (2/99)
= 99 / 2
= 49.5 hours
Therefore, it will take approximately 49.5 hours to fill the tank if the drain is left half open.