I don't know that much about BMX bikes, but according to google if they're set up for racing, they run gears in the neighborhood of 46t up front and 16t in the rear.
Assuming it's a 20" BMX bike, at 130rpm cadence that's just a little over 20mph max speed on a flat road.

I get that BMX bikes are fast off the line, but over 1/8 or 1/4 mile that advantage disappears pretty quickly. Unless I'm missing something, it should be pretty easy to take his $40. I doubt you'd even have to sprint very hard.