How many miles does a car travel using .1 of a gallon if it uses .75 of a gallon in 17.4 miles?

It will travel 2.32 miles.

This is a ratio of fuel to miles; what is required is what miles is equal to 0.1 fuel:

Fuel : miles

0.75 : 17.4

0.1 : distance

To find the distance cross multiply (creating an equation as the product of the left diagonal equals the product of the right diagonal) and solve for distance:

0.75 × distance = 17.4 × 0.1

→ distance = 17.4 × 0.1 ÷ 0.75

→ distance = 2.32