a) What is the fuel consumption in miles per gallon?

270 miles / 6 gal = 45 miles per gallon

b) How much fuel would Karen use for a journey of 405 miles?

let x represent the gallons of fuel needed for 405 miles trip

45 : 1 = 405 : x

by solving we find

x = 9 gal

click here to see the step by step solution of the equation

Karen would use 9 gallons of fuel for the 405 miles journey

c) When full,the fuel tank in Karen's car holds 12 gallons of fuel. Is it possible for her to travel 550 miles on one full tank of fuel?

since 1 gallon is needed for 45 miles

12 gallons are enough for 12*45 = 540 miles < 550 miles

it is not possible to travel 550 miles on one full tank of fuel.