Final answer:
By calculating the fuel consumption rate and applying it to the amount of fuel left, it has been determined that the racecar will have 6 gallons of fuel left after completing 96 laps.
Step-by-step explanation:
To determine after which lap the racecar will have 6 gallons left in its tank, we use the information given about fuel consumption at laps 4 and 27. We first calculate the number of laps completed and the amount of fuel consumed during these laps. After lap 4, the car has 22 gallons left, and after lap 27, it has 18 gallons left. The fuel consumption is therefore 22 - 18 = 4 gallons over 27 - 4 = 23 laps.
Next, we calculate the rate of fuel consumption per lap by dividing the total gallons consumed by the number of laps: 4 gallons / 23 laps = 4/23 gallons per lap. To find out after how many more laps the car will be left with 6 gallons, we subtract the current amount of fuel (18 gallons) by the desired amount (6 gallons) and divide by the rate of fuel consumption.
This gives us (18 - 6) / (4/23) = 12 / (4/23) = 12 * (23/4) = 69 laps. Since the car already completed 27 laps, we add 69 to find the total number of laps: 27 + 69 = 96 laps. This means that after completing 96 laps, the racecar will have 6 gallons left in its tank.