if the red river is 500 miles longer than the blue river. if the sum of their lengths is 5550 miles what is the length of each river

r = b+550

r+b = 5550

b+550 + b = 5550
2b = 5000
b = 2500
r = 3000

Let's set up a system of equations to represent the given information. Let "x" represent the length of the blue river in miles.

According to the problem, the red river is 500 miles longer than the blue river, so its length can be represented as "x + 500".

The sum of their lengths is given as 5550 miles, so we can write the equation:

x + (x + 500) = 5550

Now we can solve this equation step-by-step to find the length of each river.

1. Combine like terms: x + x + 500 = 5550
This simplifies to: 2x + 500 = 5550

2. Subtract 500 from both sides: 2x + 500 - 500 = 5550 - 500
This simplifies to: 2x = 5050

3. Divide both sides by 2 to isolate x: 2x / 2 = 5050 / 2
This simplifies to: x = 2525

Therefore, the length of the blue river is 2525 miles. And since the red river is 500 miles longer, its length would be:

x + 500 = 2525 + 500 = 3025 miles

So, the length of the blue river is 2525 miles, and the length of the red river is 3025 miles.

To find the lengths of the red and blue rivers, we can set up a system of equations based on the given information.

Let's denote the length of the blue river as "x" miles.

According to the problem, the red river is 500 miles longer than the blue river. Therefore, the length of the red river is "x + 500" miles.

We also know that the sum of their lengths is 5550 miles. So, we can write the equation:

x + (x + 500) = 5550

Now, let's solve this equation to find the length of each river.

Combine like terms:
2x + 500 = 5550

Subtract 500 from both sides:
2x = 5050

Divide both sides by 2:
x = 2525

So, the length of the blue river is 2525 miles.

To find the length of the red river, plug the value of x back into the equation:
Length of red river = x + 500 = 2525 + 500 = 3025

Therefore, the length of the red river is 3025 miles.