The hare will move 10 meters each second, so after one second, he has moved two meters. After two second, he has moved 20 meters. 3 seconds = 30 meters, and so on.

If the tortoise accelerates at 2 meters per second, he moves 2 meters the first second, 4 meters the next second, 6 meters the third second, 8 meters the second after that…

It will take the tortoise 10 seconds to catch the rabbit and 11 seconds to pass.

Here is the progression:

Rabbit: 10+10+10+10+10+10+10+10+10+10=100 meters (after 10 seconds)

+10=110 meters (after 11 seconds)

Tortoise:

2 meters the first second

2meters the first second +2 meters fatster speed=4 meters moved the next second (2 the first second+4 the next second =6 meters total moved after 2 seconds)

4+2=6 (6+6=12 meters total moved)

6+2=8 (12+8=20 meters total moved)

8+2=10 (20+10=30 total meters)

10+2=12 (30+12=42 meters)

12+2=14 (42+14=56 meters)

14+2=16 (56+16=62 meters)

16+2=18 (62+18=80 meters)

18+2=20 (80+20=100 meters after 10 seconds)

20+2=22 (100+22=122 meters after 11 seconds)

After 10 seconds, they are even again. Since the tortoise is now moving faster, it takes him only one more second to pass the hare, the answer is 11 seconds.