First of all, you can lead a horse to the water, but you can't make it drink.
Second, there can be other reasons for the other person not being as productive as you (e.g. lack of training).
That said, if the real problem is a non-cooperative coworker, one strategy is having the workload divided before start working. To let the division be as fair as possible, even if the other person is not willing to cooperate, you can do it this way:
- One person creates two sets of independent tasks.
- The other person chooses which set of tasks does she want to get done.
- Both of you start working.
The following advantages:
- Since the workload share is agreed beforehand, you set expectations on your coworker about how many work she needs to get done.
- If a person finishes REALLY SOONER (in your question, 100% sooner) than the other, chances are the division wasn't fair enough. Both of you will take that into account when dividing tasks for the next day.
- If a person finishes early, but not too much, no big deal. The early finisher can help the other one with the remaining tasks.
- If the same one person finishes REALLY SOONER than the other, everyday (e.g. five days out of five), you will have data and a clear output to feed a conversation with your manager.