https://file.aiquickdraw.com/mathbot/file/17287498303857uppdlru.jpg

The problem states that a clock strikes:

- Once at 1 o'clock,
- Twice at 2 o'clock,
- Thrice at 3 o'clock, and so on.

The information provided mentions that it takes **6 seconds to strike at 3 o'clock**. We need to find out how much time it will take to strike at **9 o'clock**.

### Understanding the Pattern:

At each hour, the number of strikes equals the hour number:
- 1 strike at 1 o'clock,
- 2 strikes at 2 o'clock,
- 3 strikes at 3 o'clock,
- …,
- 9 strikes at 9 o'clock.

For any number of strikes, the first strike occurs at time = 0 seconds, and the remaining strikes follow after equal intervals of time.

### Step-by-Step Solution:

- At **3 o'clock**, there are **3 strikes**. It takes **6 seconds** for the 3 strikes.
  - The time interval between each strike is \(\frac{6 \text{ seconds}}{2} = 3 \text{ seconds}\) per interval (because there are 2 intervals between the 3 strikes).

- At **9 o'clock**, there are **9 strikes**. The time between each strike remains the same (3 seconds per interval).
  - The total number of intervals between the 9 strikes is \(9 - 1 = 8\) intervals.
  - The total time to strike 9 times is:
    \[
    \text{Total time} = 8 \times 3 \text{ seconds} = 24 \text{ seconds}.
    \]

### Final Answer:
It will take **24 seconds** to strike at 9 o'clock.

Would you like more details, or do you have any questions?

---

Here are 5 related questions to deepen your understanding:
1. How much time will it take for the clock to strike at 12 o'clock?
2. If the interval between strikes were 4 seconds, how much time would it take to strike at 9 o'clock?
3. How much time does it take to strike at 6 o'clock with the same 3-second interval?
4. What would be the total time for striking 4 times if the interval between each strike is 5 seconds?
5. How does the number of intervals change as the hour number increases?

**Tip:** When dealing with repeated actions (like clock strikes), always count the intervals between events, not just the events themselves.

A clock strikes once at 1 o'clock, twice at 2 o'clock, and so on. If it takes 6 seconds to strike at 3 o'clock, how much time will it take to strike at 9 o'clock?

Calculate how much time it will take for a clock to strike at 9 o'clock, based on a pattern of increasing strikes. Using an interval-based approach, this problem explores arithmetic sequences and time calculations. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation