In Search of the Longest Subway Ride

What's the longest ride you can take on the New York subway? The MTA website says it's a 38-mile trip from 241st Street in the Bronx to Far Rockaway, but we think we can do better. We found a route between those same two stations that covers over 148 miles of track. It uses every subway line at least once and requires 45 transfers.

UPDATE 4:05 PM: Our 148-mile route was based on four computers checking 200 billion possibilities and counting. But using this page, someone's browser found an even longer route today: 154.6 miles with 54 transfers! We've verified that route, and mapped it here:

So what's the REAL longest ride you can take on the New York subway? We're still not sure, so maybe you can help us. See if your computer can beat the record!