Question

The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume V of the tank (in L) and the discharge rate of gasoline V (in L/s). How long will it take in minutes to fill a 14 gallon tank assuming it is completely empty? The discharge rate for the gas is 38.0 l/min.

Answer 1

To fill a tank of volume V with a constant discharge rate Q, the filling time t can be calculated using the formula t = V / Q. Using this formula and the given values, it will take approximately 0.368 minutes to fill a 14 gallon tank assuming it is completely empty.

Step-by-step explanation:

To obtain a relation for the filling time in terms of the volume V of the tank and the discharge rate of gasoline V, we can use the equation:

t = V / Q

where t is the filling time in seconds, V is the volume of the tank in liters, and Q is the discharge rate of gasoline in liters per second.

To convert the discharge rate from liters per minute to liters per second, we divide by 60 since there are 60 seconds in a minute. So, the discharge rate in liters per second is 38.0 l/min / 60 = 0.633 l/s.

Now we can substitute the values into the equation:

t = 14 L / 0.633 l/s = 22.1 s

Finally, to convert the filling time from seconds to minutes, we divide by 60 since there are 60 seconds in a minute:

t = 22.1 s / 60 = 0.368 min

Therefore, it will take approximately 0.368 minutes to fill a 14 gallon tank assuming it is completely empty.

Answer 2

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.

Step-by-step explanation:

The filling time of a gas tank can be given by a first order function in this format:

`F(t) = V - r*t`

In which
`F(t)` is the current amount of fuel in the tank(in L),
`V` is the volume of the tank(in L),
`r` is the discharge rate of the tank(in L/s) and t is the time in seconds.

Finding the values of the parameters:

The tank is completly empty, so
`F(t) = 0`.

The volume of the tank is 14 gallons. However, the problem states that the volume of the tank is measured in liters.

Each gallon has 3.78L.

So
`V = 14*3.78 = 53L`

The discharge rate for the gas is 38.0 l/min. However, the problem states that the discharge rate is in L/s. So, to find the value of r, we solve the following rule of three.

38 L - 60s

r L - 1s

`60r = 38`

`r = (38)/(60)`

`r = 0.63`

Solving the equation:

`F(t) = V - r*t`

`0 = 53 - 0.63t`

`0.63t = 53`

`t = (53)/(0.63)`

`t = 84.12s`

It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.