an empty 50 gallon is filled with water by faucet with a rate 4 gallon per min while it can be drain by a faucet at the bottom of the drum by half a gallon per minute . how long will it take the faucet to fill the drum up to brim if at the same time the faucet at the bottom is open`
net inflow is 4 - 1/2 = 7/2 gal/min
So, it takes 50/(7/2) = 14.3 min to fill
tnx
To solve this problem, we need to understand the rate at which the water level in the drum changes.
The filling rate of the faucet is 4 gallons per minute, while the draining rate of the faucet at the bottom is 0.5 gallons per minute (half a gallon per minute).
Now let's calculate the net rate of filling the drum by subtracting the draining rate from the filling rate:
Net rate of filling = Filling rate - Draining rate
= 4 gallons per minute - 0.5 gallons per minute
= 3.5 gallons per minute
Therefore, the drum is being filled at a net rate of 3.5 gallons per minute.
To find out how long it will take to fill the drum up to the brim, we need to know the capacity of the drum. In this case, it is given as 50 gallons.
Time = Capacity / Filling Rate
= 50 gallons / 3.5 gallons per minute
= 14.29 minutes
So, it will take approximately 14.29 minutes (or approximately 14 minutes and 17 seconds) to fill the drum up to the brim while the bottom faucet is open.