Two cars start from the same point at the same time. One car travels north at 62.0 miles per hour. The other car travels east at 55 miles per hour. How far apart, to the nearest mile, are the cars after 1.5 hours?

After 1.5 hours, the car traveling north has traveled $1.5\times {62} = 93$ miles. The car traveling east has traveled $1.5\times {55} = 82.5$ miles. The cars form a right triangle, and the distance between them can be found with the Pythagorean Theorem. The distance between the cars is $\sqrt{93^2 + 82.5^2}$, which to the nearest mile is $\boxed{121}$ miles.