Ok, I did it for 28 mph in a 10 mph wind. Again, ignoring friction.
If the cart moves at 28 mph, the propeller spins at 133.7 RPM or 2.228 rev/s. The airspeed of the cart is 18 mph, or 26.4 ft/s. And the diameter of the propeller is 16 ft. So, the advance ratio (jj) is 26.4/[(2.228)(16)] = 0.7406.
To get values for the coefficients ct and cq, I interpolated linearly between the two nearest values of jj given (0.7073 and 0.8252), and ended up with ct = 0.0834 and cq = 0.0120.
Then, the forward thrust of the propeller works out to be 61.32 lb, the torque driving the propeller is 141.2 ft-lb, and the backward force of the ground on the wheels is 48.11 lb.
That leaves 13.21 lb to overcome friction and accelerate the cart.