The rms speed is given as. v_rms = [3RT/M]^1/2

        where M is the molar mass,

                  T is the temperature and

                  R is a constant.

At same temperature, the speed ratios would be

v_{rms (}oxygen) / v_{rms (hydrogen)} = [M_hydrogen / M_oxygen]^1/2 as the 3RT terms cancel out from the numerator and denominator

When we take the molar mass of hydrogen and oxygen to be 1 and 16 respectively then,

v_{rms (}oxygen) / v_{rms (hydrogen)} = [1/16]^1/2 = ¼