A frog was at the bottom of a 12-meter hole. Each day it climbed up 3 meters but always slid back 2 meters. How many days will take the frog to get out of the hole?
it gains 1 meter each day.
After 9 days it has climbed 9 meters
On the 10th day it climbs 3 meters and is out.
10
To determine the number of days it will take for the frog to get out of the hole, we need to calculate the net distance the frog climbs each day until it reaches or surpasses the top of the hole.
1. On the first day:
- The frog climbs up 3 meters.
- The net distance climbed is 3 meters (3 - 2).
2. On the second day:
- The frog climbs up 3 meters.
- The net distance climbed is now 6 meters (3 + 3 - 2).
3. On the third day:
- The frog climbs up 3 meters.
- The net distance climbed is now 9 meters (6 + 3 - 2).
4. On the fourth day:
- The frog climbs up 3 meters.
- The net distance climbed is now 12 meters (9 + 3 - 2).
Since the frog reaches the top of the hole on the fourth day, it will take the frog 4 days to climb out of the 12-meter hole.
To find out how many days it will take for the frog to get out of the hole, we need to determine the number of times it can climb up and slide back before reaching the top.
Let's break down the process step by step:
1. On the first day, the frog climbs up 3 meters. The total distance covered by the frog at this point is 3 meters.
2. On the second day, the frog climbs up 3 meters again. The total distance covered by the frog is now 3 + 3 = 6 meters.
3. On the third day, the frog climbs up 3 meters once more. The total distance covered by the frog is now 6 + 3 = 9 meters.
4. On the fourth day, the frog climbs up 3 meters as usual, but it then slides back 2 meters. Therefore, the total distance covered is 9 + 3 - 2 = 10 meters.
5. On the fifth day, the frog repeats the process, climbing up 3 meters and then sliding back 2 meters. The total distance covered is now 10 + 3 - 2 = 11 meters.
At this point, the frog is just 1 meter away from reaching the top of the hole. On the sixth day, the frog climbs up 3 meters and successfully escapes the hole.
Therefore, it will take the frog 6 days to get out of the hole.