An ant tries to climb the water pipe 10m high, it climb 2m up and slips back 1m down in every moves. In how many will it reach the top of the 10m high pipe.
The water pipes 10m high
It climb 2m up
and slips back 1m down in every moves.
8+2=10
• so the 9th move ant reach the top 10m water pipe high
At move #1, reaches 2 m, ends up at 1 m
At move #2, reaches 3 m, ends up at 2 m
At move #3, reaches 4 m, ends up at 3 m
....
At move #9, reaches 10 m
you are correct
To find out how many moves it will take for the ant to reach the top of the 10m high pipe, we can analyze the pattern of its climbs and slips.
Initially, the ant starts at 0m and climbs 2m, reaching a height of 2m. The ant then slips back 1m, bringing it down to a height of 1m. This process of climbing 2m and slipping 1m down repeats until the ant reaches a height of 10m.
Let's break it down step by step:
- After the first climb, the ant is at a height of 2m.
- After the first slip, the ant is at a height of 1m.
- After the second climb, the ant is at a height of 3m.
- After the second slip, the ant is at a height of 2m.
- After the third climb, the ant is at a height of 4m.
- After the third slip, the ant is at a height of 3m.
From this pattern, we observe that the ant is climbing upward by 2m in every two moves. However, after every two moves, the ant slips back 1m. Therefore, in every two moves, the ant makes a net progress of 1m.
To calculate the number of times the ant needs to make this 2-move cycle, we can divide the height of the pipe (10m) by the net progress (1m) in each cycle:
10m ÷ 1m = 10
So, the ant will need to make a total of 10 cycles to reach the top of the pipe.
Since each cycle consists of 2 moves (a climb and a slip), we multiply the number of cycles by 2 to get the total number of moves:
10 cycles × 2 moves/cycle = 20 moves
Therefore, it will take the ant 20 moves to reach the top of the 10m high pipe.