Io is in a circular orbit so there is a centripetal force acting on it. This centripetal force is the gravitational force Jupiter exerts on it.
Fg=Fc
G(M*m)/r^2 = m*ac,
where G is the universal constant of gravitation = 6.67*10^(-11) [m^3*kg^.1*s^-2],
M is Jupiter's mass,
m is Io's mass,
r is the distance between Io and Jupiter,
and ac is the centripetal acceleration which equals v^2/r, where v is the linear Io's speed and r is the radius of the orbit, in this case the distance between Io and Jupiter.
Substituting ac=v^2/r in the formula above and rearranging gives v=√(GM/r).
Plug in numbers to find v=17329.4 m/s.
