Sorry, I am not sure what I am looking at here. Would need details on how the scene is set up, what is meant by with background, what the object is, why it's white in one render and black in another (different material?). For now it looks like one has no lighting (assuming the white object is a static white color, not emitting light), and one has lighting, and of course if calculating lighting then things will take longer. We'd also need to know what kind of time difference you are talking about, especially the render time for the second image (if the first has no lighting at all, render times would be expected to be insanely fast as the render engine doesn't really have to do anything :) ).
EDIT, I see the times now :) Still looks to me like the first has no lighting, and the second has lighting and even transparency, it would be expected that with no lighting it would take virtually no time at all since the engine doesn't have to do anything. On the second, would need to know what the engine is being asked to do though so would need info on the scene set up and lighting set up and materials.
