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

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:

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

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

$60r = 38$

$r = \frac{38}{60}$

$r = 0.63$

Solving the equation:

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

$0 = 53 - 0.63t$

$0.63t = 53$

$t = \frac{53}{0.63}$

$t = 84.12s$

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