Question

What is the ratio of the speed of methane gas to the speed of sulfur dioxide gas if both gases ate at the same pressure and temperature?

Answer 1

Roughly, if you consider all KE in a gas to be translational, and for monatomic gases, that is mostly true, then Temp is a measure of avg KE (and KE = constant*v^2)

Methane CH3
Sulfur Dioxide SO2
Now notice these are not monatomic gases, so the assumption falls apart. There will be some KE in vibration, and rotation. But I assume your teacher wants you to ignore that. If not, your question was very poorly worded.

So the ratio of mass in SO2 to CH3 is
64/15

speedmethane^2 * 15*k=speedSO2^2*64*k

speedmethane/speedSO2= sqrt (64/15)

I want to assure you real life is much more complex than this.