To solve the problem of how much time the monkey requires to climb a 60 m high pole, we can break down the problem step by step.
### Step 1: Determine the net distance climbed in 2 minutes
In the first minute, the monkey climbs 6 meters. In the second minute, it slips down 3 meters. Therefore, in 2 minutes, the net distance climbed is:
\[
\text{Net distance in 2 minutes} = \text{Climb} - \text{Slip} = 6 \, \text{m} - 3 \, \text{m} = 3 \, \text{m}
\]
### Step 2: Calculate the effective distance climbed per minute
From the previous calculation, we see that the monkey climbs 3 meters every 2 minutes. Therefore, the effective distance climbed per minute is:
\[
\text{Effective distance per minute} = \frac{3 \, \text{m}}{2 \, \text{min}} = 1.5 \, \text{m/min}
\]
### Step 3: Calculate the distance before the last climb
Since the monkey climbs 6 meters in the first minute, we need to find out how many complete cycles of 2 minutes it takes to reach a point close to the top. The monkey will continue this cycle until it is within 6 meters of the top (60 m):
Let \( x \) be the number of complete 2-minute cycles. The distance climbed after \( x \) cycles is:
\[
\text{Distance climbed} = 3x \, \text{m}
\]
We need to find \( x \) such that:
\[
3x < 60 - 6 \quad \text{(to leave room for the final climb)}
\]
This simplifies to:
\[
3x < 54 \quad \Rightarrow \quad x < 18
\]
So, the maximum integer value for \( x \) is 17.
### Step 4: Calculate the total distance climbed after 17 cycles
The total distance climbed after 17 cycles is:
\[
\text{Total distance} = 3 \times 17 = 51 \, \text{m}
\]
### Step 5: Determine the remaining distance to climb
After 17 cycles, the monkey has climbed 51 meters. The remaining distance to the top is:
\[
\text{Remaining distance} = 60 \, \text{m} - 51 \, \text{m} = 9 \, \text{m}
\]
### Step 6: Calculate the time taken to climb the remaining distance
In the next minute, the monkey will climb 6 meters. After climbing 6 meters, the monkey will be at:
\[
51 \, \text{m} + 6 \, \text{m} = 57 \, \text{m}
\]
At this point, the monkey will still need to climb 3 more meters to reach the top. In the following minute, the monkey will climb these remaining 3 meters, reaching the top of the pole.
### Step 7: Calculate the total time taken
The total time taken is:
- Time for 17 cycles (2 minutes each) = \( 17 \times 2 = 34 \, \text{minutes} \)
- Time for the last climb (2 additional minutes) = 1 minute for the first 6 meters and 1 minute for the last 3 meters.
Thus, the total time taken is:
\[
\text{Total time} = 34 + 1 + 1 = 36 \, \text{minutes}
\]
### Final Answer
The monkey requires **36 minutes** to reach the top of the 60 m high pole.
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