Final answer:
To determine the heights of the two towers, we let the height of the shorter tower be x feet and set up the equation 2x + 724 = 1918. By solving the equation, we find that the shorter tower is 597 feet tall, and the taller tower is 1321 feet tall.
Step-by-step explanation:
Let's solve the problem of finding the heights of two towers with the given information.
According to the question, the height of one tower is 724 feet more than the other, and their combined height is 1918 feet. Let's denote the height of the shorter tower as x feet.
Therefore, the height of the taller tower would be x + 724 feet.
Now we can create an equation representing their total height: x (shorter tower) + (x + 724) feet (taller tower) = 1918 feet.
Simplifying this equation, we get 2x + 724 = 1918.
To find the value of x, we subtract 724 from both sides of the equation, which gives us 2x = 1194.
Dividing both sides by 2, we get x = 597.
Therefore, the height of the shorter tower is 597 feet, and the taller tower, being 724 feet higher, is 1321 feet tall.