Forza Motorsport 5

Long Beach has three different options regarding which sections of the track to race on, but you need to race on the Full Circuit track which is 1.97 miles long. That means you'll need to make 153 laps total in your modern indy car (if the game is tracking mileage correctly).

There are a total of 4 Modern Indy cars available for 1.3 million credits each:

Chevrolet Dallara DW12 Andretti Autosport #1
Chevrolet Dallara DW12 Team Penske #12
Honda Dallara DW12 Target Chip Ganassi #9
Honda Dallara DW12 Rahal Letterman Lanigan Racing #15

These are high-powered X-class cars with a 999 rating. It is a big investment, but
you can use your modern indy car in the modern indy car career event (Racing League). The Long Beach full circuit track is the second event and is 5 laps, so you'll get about 10 miles each time you race it. You'll have to complete the rest of the championship (10 races), but afterwards you can continue to race in that career event 20 times total for around 200 miles and the following achievement:



While we're at it, why not stack up on a few other achievements? You might want to use your indy car for the Long Beach customs achievement:



That would get you at least 50 miles if you do only one lap.

Use your indy car in the Long Beach Full Circuit in a rivals event for this achievement:



That'll get you another 50 miles if you do only one lap at a time.

Beach Hopper offers another way to earn more miles (thanks Parallax Demon):



That'll be around 100 miles if you do one lap at a time. You can set up a private multiplayer lobby for this.

The following is an expired challenge and no longer relevant to the solution:


Have fun! Get creative! Perhaps you can get an affinity level to 25 with Honda or Chevy. It is quite nice when you can stack up on some achievements. Enjoy!