What would you estimate to be the speed of a galaxy located 60 million light-years away?

Multiply the Hubble constant by the distance. That will give you an average value.

For the Hubble constant (which is not really a constant), see
http://scienceworld.wolfram.com/physics/HubbleConstant.html

You may have to convert light years to megaparsecs

In practice, it is easier to measure the speed directly from the Doppler shift of spectral lines, than it is the to measure the distance.