In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15m high.

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.

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