In 6 weeks' time there will be a drama competition. The school drama group had already spent two weeks and 6 days rehearsing. How much time is left before the competition?

Total time until competition = 6 weeks
Time spent rehearsing = 2 weeks and 6 days

Since 1 week = 7 days, we can write 6 weeks as 5 weeks and 7 days.

Subtract days: $7 \text{ days} - 6 \text{ days} = 1 \text{ day}$
Subtract weeks: $5 \text{ weeks} - 2 \text{ weeks} = 3 \text{ weeks}$

The time left before the competition is 3 weeks and 1 day.

The final answer is $\boxed{\text{3 weeks and 1 day}}$.

:

First period = 5 weeks and 3 days
Second period = 1 week and 6 days

Total weeks = $5 \text{ weeks} + 1 \text{ week} = 6 \text{ weeks}$
Total days = $3 \text{ days} + 6 \text{ days} = 9 \text{ days}$

Since 1 week = 7 days, 9 days can be written as 1 week and 2 days.
Total time = $6 \text{ weeks} + 1 \text{ week} + 2 \text{ days} = 7 \text{ weeks and 2 days}$

The total time they cared for animals is 7 weeks and 2 days.

The final answer is $\boxed{\text{7 weeks and 2 days}}$.