Question

if a bathtub has 100 gallons of water, while 10 gallons of water is coming in through the faucet and 10 gallons of water is going out through the drain per minute, what should be the residence time of water in the bathtub?

Answer 1

The residence time of water in a bathtub with 100 gallons capacity and an inlet and outlet flow rate of 10 gallons per minute each would be 10 minutes.

Step-by-step explanation:

The question involves calculating the residence time of water in a bathtub with specific inflow and outflow rates. Residence time, in this context, refers to the average time water spends in the bathtub before exiting through the drain.

Residence Time Calculation

To calculate the residence time of water in a bathtub when the inflow and outflow rates are equal, we can use the formula:

Residence Time = Volume of water in bathtub / Rate of water flow

Given that the bathtub holds 100 gallons of water, and both the inflow and outflow rates are 10 gallons per minute, the residence time can be calculated as follows:

Residence Time = 100 gallons / 10 gallons per minute = 10 minutes

Therefore, the residence time of water in the bathtub will be 10 minutes. This means, on average, a gallon of water will spend 10 minutes in the bathtub before it is drained out, provided that the input and output flows remain constant at 10 gallons per minute.