Question

What is the ratio of the length of one pole to the total length of two poles, given that the ratio of the length of Pole A to Pole B is 4:5?

Answer 1

Let the length of Pole A be \( 4x \) and the length of Pole B be \( 5x \), where \( x \) is a common factor.

Now, we can find the total length of both poles:

\[
\text{Total length} = \text{Length of Pole A} + \text{Length of Pole B} = 4x + 5x = 9x.
\]

Next, we want to find the ratio of the length of one pole to the total length of two poles. We can do this for both poles.

1. For Pole A:
\[
\text{Ratio of Pole A to Total Length} = \frac{\text{Length of Pole A}}{\text{Total Length}} = \frac{4x}{9x} = \frac{4}{9}.
\]

2. For Pole B:
\[
\text{Ratio of Pole B to Total Length} = \frac{\text{Length of Pole B}}{\text{Total Length}} = \frac{5x}{9x} = \frac{5}{9}.
\]

Hence, the ratio of the length of one pole (Pole A) to the total length of both poles is

\[
\frac{4}{9}.
\]

The final answer is

\(\frac{4}{9}\) (for Pole A)

And for Pole B, it is

\(\frac{5}{9}\).