Moral Dilemmas

I'm currently reading Justice: What's The Right Thing To Do?, and it starts with a couple of hypothetical situations that has really bothered me because it demonstrates a big inconsistency in our conscience.

Scenario #1: You are on a trolley heading down a track, and you notice that there are 5 people tied to the rails ahead. The brakes are out, but you can turn onto a different track where there is only 1 person tied down. So your only choices are to do nothing and let the trolley kill 5 people, or change course and kill 1 person that would have otherwise lived. What's the right thing to do? For most people (including myself), your conscience tells you that the best thing is to change course and save the greatest number of lives.

Scenario #2: Same case, but there's nobody in the trolley. You and a very heavy person are on a bridge overlooking the track. If you do nothing, the 5 people on the track will die. But you happen to know that if you push the heavy person off the bridge and onto the track, he will die when the train hits him, but it will cause the train to stop. It would do no good for you to jump down. What is the right thing to do? For most people (including myself), your conscience tells you that you should not push the innocent bystander off the bridge.

The problem is that these 2 scenarios are effectively the same moral dilemma. In both cases you can do nothing and let 5 people die, or make a choice where the trolley hits and kills only 1 person that would have lived otherwise. So what really is the right thing to do, and why does our conscience contradict itself? I don't know. But I assume our different gut reactions have a lot to do with how directly responsible we'd feel for the 1 person that died in each case. Pushing someone off a bridge feels like you're directly killing someone whereas you feel more removed from the situation if you just turn a train. Like how people can be complete jerks when driving but you know they'd be nice to your face.