Answer :
To find out how long the completed runway will be, we'll use the information provided:
1. We know that [tex]\(\frac{5}{8}\)[/tex] (five-eighths) of the runway has been built, and this portion is 2 kilometers long.
2. To find the total length of the runway, we need to determine what the whole (or 8/8) of the runway would be. We can set up a proportion to solve for the total length.
- Since [tex]\(\frac{5}{8}\)[/tex] of the runway corresponds to 2 kilometers, we can think of it as a fraction of the whole length:
[tex]\[
\frac{5}{8} \times \text{(Total Length)} = 2 \text{ km}
\][/tex]
3. To find the total length, we'll divide the 2 kilometers by the fraction [tex]\(\frac{5}{8}\)[/tex]:
[tex]\[
\text{Total Length} = \frac{2 \text{ km}}{\frac{5}{8}}
\][/tex]
4. Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
[tex]\[
\text{Total Length} = 2 \text{ km} \times \frac{8}{5}
\][/tex]
5. Performing the multiplication:
[tex]\[
\text{Total Length} = 2 \times \frac{8}{5} = \frac{16}{5} \text{ km} = 3.2 \text{ km}
\][/tex]
So, the completed runway will be 3.2 kilometers long.
1. We know that [tex]\(\frac{5}{8}\)[/tex] (five-eighths) of the runway has been built, and this portion is 2 kilometers long.
2. To find the total length of the runway, we need to determine what the whole (or 8/8) of the runway would be. We can set up a proportion to solve for the total length.
- Since [tex]\(\frac{5}{8}\)[/tex] of the runway corresponds to 2 kilometers, we can think of it as a fraction of the whole length:
[tex]\[
\frac{5}{8} \times \text{(Total Length)} = 2 \text{ km}
\][/tex]
3. To find the total length, we'll divide the 2 kilometers by the fraction [tex]\(\frac{5}{8}\)[/tex]:
[tex]\[
\text{Total Length} = \frac{2 \text{ km}}{\frac{5}{8}}
\][/tex]
4. Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
[tex]\[
\text{Total Length} = 2 \text{ km} \times \frac{8}{5}
\][/tex]
5. Performing the multiplication:
[tex]\[
\text{Total Length} = 2 \times \frac{8}{5} = \frac{16}{5} \text{ km} = 3.2 \text{ km}
\][/tex]
So, the completed runway will be 3.2 kilometers long.
