Presumably the engine was only idling during their decent if the only thing that slowed their car was 'miraculously' grinding the car against the mountainside.
So, using previous records, they should estimate fuel usage during the decent. Then they should walk to the nearest fuel station, purchase fuel, and walk back. During that time, they can calculate the amount of fuel that will evaporate while they have the gas cap off and the amount of fuel that will stick to the walls of the piping between the gas cap and the fuel tank. This way when they return to the car, they can put in almost exactly the amount of fuel that was consumed during their harrowing stop.
This presumes the fuel station has the same mixture as they have in their tank. Otherwise all bets are off and they should simply give up.
