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Including bike?
http://felixwong.com/2015/07/how-much-does-it-cost-to-do-the-trans-am-bike-race/
$3000-4000 depending on how you cut it. Other people will be more/less expensive depending on their airline tickets, how often they bivvy vs. hotel, how fast they ride it - faster riders might have more expensive kit but they will be riding/eating for fewer days and possibly using fewer hotel stops. Short answer: no idea, but probably pretty expensive for me.
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Including bike?
Yeah. Rough breakdown:
Flights £850 plus £150 to change the return flight date (British Airways, LHR > YYC, PHX > LHR)
Food, Lodging and Mechanicals en route: £1600
Extraction from Antelope Wells to Phoenix £400 (shuttle ride, and cousins hiring car for a few days).
Bike, bags, dynamo kit, etc £3000ishWorlds most expensive free race.
Tour Divide is free.
Cost me about £5k all in.