Question

river c is 100 miles longer than river d. if the sum of their lengths is 5,560 miles, what is the length of each river?
the length of river c is □ miles, and the length of river d is □ miles.

Explanation:

Step1: Define variables for lengths

Let $x$ = length of River D (miles). Then length of River C = $x + 100$ miles.

Step2: Set up sum equation

Sum of lengths equals 5560:
$$x + (x + 100) = 5560$$

Step3: Simplify and solve for $x$

Combine like terms, isolate $x$:
$$2x + 100 = 5560$$
$$2x = 5560 - 100 = 5460$$
$$x = \frac{5460}{2} = 2730$$

Step4: Find length of River C

Substitute $x$ into River C's expression:
$$x + 100 = 2730 + 100 = 2830$$

Answer:

The length of River C is 2830 miles, and the length of River D is 2730 miles.