A monkey wants to climb up a pole. He climbs 12 metres in 1 minute and
then he slips back 3 metres in the next
minute. If the pole is 63 metres high, how
long does he take to climb at the top of
the pole?

To determine how long it takes for the monkey to reach the top of the 63-meter high pole, we can break the problem into a step-by-step analysis of the monkey's progress.

### Calculation:

1. **Effective Climb per 2 Minutes:**
   - The monkey climbs 12 meters in the first minute.
   - The monkey slips back 3 meters in the second minute.
   - Therefore, in 2 minutes, the monkey effectively climbs \( 12 - 3 = 9 \) meters.

2. **Total Effective Distance:**
   - Let's see how many full 9-meter segments the monkey needs to cover:
     - \( 63 \div 9 = 7 \)
   - So, the monkey effectively climbs 9 meters in each 2-minute cycle.

3. **Time Calculation:**
   - To reach 54 meters (which is \( 9 \times 6 \) meters):
     - 6 cycles are needed, and each cycle is 2 minutes.
     - \( 6 \times 2 = 12 \) minutes.
   - After 54 meters, the monkey is just 9 meters away from the top.
   - In the next minute, the monkey climbs the remaining 9 meters without slipping back.

Therefore, the monkey climbs the final 9 meters in 1 more minute, making the total time:

\[ 12 \text{ minutes} + 1 \text{ minute} = 13 \text{ minutes} \]

### Conclusion:
The monkey takes a total of **13 minutes** to climb to the top of the 63-meter high pole.

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Would you like further details or have any questions?

Here are 8 related questions to explore further:
1. What if the pole was 100 meters high, how long would it take?
2. How would the problem change if the slip was 5 meters instead of 3 meters?
3. What if the monkey rested for 1 minute every 5 meters climbed?
4. Can you calculate the monkey's average speed over the entire climb?
5. How would you model this problem using a programming language?
6. What if the monkey climbed faster each subsequent minute?
7. How would a change in climb and slip rates affect the overall time?
8. How can this problem be visualized using a graph?

**Tip:** Breaking down problems into smaller, manageable parts can simplify complex calculations and lead to more accurate solutions.

Explore how long it takes for a monkey to climb a 63-meter pole, analyzing its climbing and slipping rates. This math problem involves arithmetic and rates, suitable for Grades 5-7 students.

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