A large truck has two fuel tanks, each with a capacity of 150 gallons. Tank 1 is half full, and Tank 2 is empty.Fuel is pumped into the tanks until both tanks are full. The pump delivers fuel at a constant rate of 5 3/4 gallonsper minute. 1) Write an equation for the total number of gallons of fuel, g, in the two tanks in terms of the time, t, inminutes, that the pump has been filling the tanks. 2) How much fuel is in the tanks after the pump has been delivering fuel for 8 minutes?

Answer:1) [tex]G(t) = 75 + \frac{23}{4}t\\[/tex]2) After 8 minutes delivering fuel the tanks will have 121 gallons of fuelStep-by-step explanation:1) For generating the equation we have to take into account that in the tanks there is a initial volume of fuel that corresponds to 75 gallons, as it is stated that tank one is half full. As the capacity for tank 1 is of 150 gallons, half of the tank equals to: [tex]\frac{150}{2} = 75 gallons[/tex]Now we have to convert the rate of delivery that is expressed as a mixed number to an improper fraction so:[tex]5\frac{3}{4} = \frac{(5x4)+3}{4} = \frac{23}{4}[/tex]Then the pumping rate is of 23/4 gallons per minute, to get how many gallons are in the tank we just need to multiply this rate by the time in minutes, and as there is an initial volume we have to add it, so we have the following equation:[tex]G(t) = 75 + \frac{23}{4}t\\[/tex]2) To know how much fuel is in the tank after 8 minutes we have to replace this time in the previous equation so we have[tex]G(t) = 75 + \frac{23}{4}t\\G(8) = 75 + \frac{23}{4}(8)\\G(8) = 75 + 23(2)\\G(8) = 75 + 46\\G(8) = 121 gallons[/tex]After 8 minutes delivering fuel the tanks will have 121 gallons of fuel