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------------------------------------------------ The local airport has two runways, A and B. The total length of the runways is 20,500 feet, and the difference in their lengths is 5,500 feet. How long is each runway?

To determine the lengths of the two runways, we use a system of equations. Runway A is 13,000 feet long and runway B is 7,500 feet long, solved by setting up and solving a pair of linear equations based on the given total length and the difference in lengths.

To find the lengths of the two runways (A and B) at the local airport, we can use a system of linear equations.

From the problem statement, we know that the sum of the lengths of runways A and B is 20,500 feet, and the difference between their lengths is 5,500 feet.

We can express this information as two equations:

Equation 1: A + B = 20,500

Equation 2: A - B = 5,500

Now, we can add both equations together to eliminate variable B. This results in:

2A = 26,000

Dividing both sides by 2 gives the length of runway A:

Runway A: A = 13,000 feet

To find the length of runway B, we can substitute the value of A into either Equation 1 or Equation 2. Using Equation 1:

13,000 + B = 20,500

Runway B: B = 7,500 feet

Therefore, runway A is 13,000 feet long and runway B is 7,500 feet long.