40 minutes for 6 miles? Hell, people can run faster than that.
Sad, but true. I would not say I am in any kind of phenominal shape but I am training to run a half marathon next weekend. This weekend I ran 12 miles in 1:35:00 - that works out to 7:51/per mile. Biking at 6:40/mile is slower than a lot of guys run half or even full marathons.
If I were you I would at least borrow a better bike and do some rides to see how much of a difference it makes. Then get some miles under your belt and I bet the time just gets better and better.
Good luck!