Question:
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15m high. If the length of the ship is 35 metres, how long is the model ship?
Solution:
Let $x \mathrm{~m}$ be the length of the model of the ship. Then, we have:
$1 \mathrm{~m}=100 \mathrm{~cm}$
Therefore, $15 \mathrm{~m}=1500 \mathrm{~cm}$
$35 \mathrm{~m}=3500 \mathrm{~cm}$
| Length of the mast (in cm) | Length of the ship (in cm) | |
| Actual ship | 1500 | 3500 |
| Model of the ship | 9 | x |
Clearly, if the length of the actual ship is more, then the length of the model ship will also be more.
So, this is a case of direct proportion.
Now, $\frac{1500}{9}=\frac{3500}{x}$
$\Rightarrow x=\frac{3500 \times 9}{1500}$
$\Rightarrow x=21 \mathrm{~cm}$
Therefore, the length of the model of the ship is 21 cm.