this wouldn't have been a problem if you had known how the formula is derived, instead of taking it as it is.
So basically, the gravitational potential energy of an object of mass M on the surface of the earth is -63m Million joules. Since the potential energy at infinity is 0, you need to increase the total energy of the object to 0 so that it can eventually escape the earth's field. This means that you need to give the object a k.e of +63M million joules. Using the kinetic energy formula, the M's cancel out, and the velocity found is 11.2 km/s.
Now, when you triple the velocity, you increase the kinetic energy 9 times. this means that you gave it a total k.e of 9x (63M million joules). At infinity, 63M million J will have been converted into gravitational potential energy, leaving the object with a kinetic energy of 8x(63M million Joules). You can find the velocity corresponding to this, which is about 32 km/s.
I tried to dumb this down as much as I could because the error in your understanding is pretty fundamental and can cause huge problems later on. You were directly subtracting the velocity when instead you were supposed to be subtracting kinetic energies. Essentially, you were calculating A-B instead of Sqrt( A^2-B^2), which I'm sure you are aware are completely different things