In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15 m high. If the length of the ship is 35 metres, how long is the model ship?

Answer

To solve the problem step by step, we will use the concept of direct proportions. Here’s how we can find the length of the model ship based on the given information.

### Step-by-Step Solution:

1. **Convert Measurements to the Same Unit**:
- The height of the actual ship's mast is given as 15 m. We need to convert this to centimeters.
- \( 15 \text{ m} = 15 \times 100 = 1500 \text{ cm} \)

2. **Identify the Proportions**:
- We have the height of the model ship's mast as 9 cm and the height of the actual ship's mast as 1500 cm.
- We can set up a proportion based on the heights:
\[ \frac{\text{Model Height}}{\text{Actual Height}} = \frac{\text{Model Length}}{\text{Actual Length}} \]
- Let the length of the model ship be \( x \) cm and the actual length of the ship is given as 35 m, which we also need to convert to centimeters:
- \( 35 \text{ m} = 35 \times 100 = 3500 \text{ cm} \)

3. **Set Up the Proportion**:
- Now we can set up the proportion:
\[ \frac{9 \text{ cm}}{1500 \text{ cm}} = \frac{x \text{ cm}}{3500 \text{ cm}} \]

4. **Cross-Multiply to Solve for \( x \)**:
- Cross-multiplying gives us:
\[ 9 \times 3500 = 1500 \times x \]
- Calculate \( 9 \times 3500 \):
\[ 9 \times 3500 = 31500 \]
- Thus, we have:
\[ 31500 = 1500x \]

5. **Solve for \( x \)**:
- Divide both sides by 1500 to isolate \( x \):
\[ x = \frac{31500}{1500} \]
- Calculate \( \frac{31500}{1500} \):
\[ x = 21 \]

6. **Conclusion**:
- The length of the model ship is \( 21 \text{ cm} \).

### Final Answer:
The length of the model ship is **21 cm**.