You could take a page out of the beginning runners guides for this - they generally do a run/walk combination to get you going. If you go to Cool Running for something like their couch-to-5K you'll see how they progress a beginner runner and what the run-walk ratios are. Since there is no pounding in cycling, you could probably progress a lot faster.
On the other hand, she can probably ride for many more than 7 mins now (even 30), but mentally doesn't know it and isn't used to pushing through the "I'm done now" feelings. Just a guess. For comparison, if you were on a nice vacation and rented bikes to circle the lake and it would take you about 30 mins to do so - think it would happen?
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