Answer

I think group A will solve it quicker than B.
When group A solve this problem, they want the reward quicker. If there are another challenger, they group A will work harder to get the rewards, so the problem is just a process, and thier purpose is to get reward.
On the contrary, group B enjoy solving the problem, so their purpose is to enjoy it, so time is not prblem for them.
So I think group A will solve it quicker than B.