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: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:[tex]F(t) = V - r*t[/tex]In which [tex]F(t)[/tex] is the current amount of fuel in the tank(in L), [tex]V[/tex] is the volume of the tank(in L), [tex]r[/tex] 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 [tex]F(t) = 0[/tex].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 [tex]V = 14*3.78 = 53L[/tex]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 - 60sr L - 1s[tex]60r = 38[/tex][tex]r = \frac{38}{60}[/tex][tex]r = 0.63[/tex]Solving the equation:[tex]F(t) = V - r*t[/tex][tex]0 = 53 - 0.63t[/tex][tex]0.63t = 53[/tex][tex]t = \frac{53}{0.63}[/tex][tex]t = 84.12s[/tex]It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.