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
every hour it fills 1/9 and drains 1/22
1/9-1/22 = 13/198
So, it will take 198/13 = 15.23 hours
To determine how long it will take to fill the tank if the drain is left half open, we need to consider the rates at which the tank is being filled and drained.
First, let's find the rates of filling and draining.
If the tank is filled in 9 hours, then the filling rate is 1/9 of the tank's capacity per hour. Similarly, if the tank is drained in 11 hours, then the draining rate is 1/11 of the tank's capacity per hour.
Now, if the drain is left half open, it means that the draining rate is reduced by half. Therefore, the new draining rate would be 1/22 of the tank's capacity per hour.
To calculate the overall rate of filling, we need to subtract the draining rate from the filling rate.
Filling rate - Draining rate = 1/9 - 1/22
To get a common denominator, we multiply the two fractions:
(22/22)(1/9) - (9/9)(1/22) = 22/198 - 9/198 = 13/198
So, the overall rate of filling the tank when the drain is left half open is 13/198 of the tank's capacity per hour.
To find out how long it would take to fill the tank under these conditions, we can set up the equation:
Time = Tank Capacity / Overall Rate of Filling
However, we don't have information about the tank capacity, so we cannot determine the exact time.