Final answer:
By setting the expressions for PR and RS equal, since R is the midpoint, and solving for x, we find that x equals 3, which makes the length of RS 16 meters.
Step-by-step explanation:
The question asks for the length of RS given that R is the midpoint of PS, and the lengths PR and RS are described by the expressions 7x - 5 and 4(x + 1), respectively. Since R is the midpoint, PR is equal to RS. Setting the expressions for PR and RS equal to each other gives us an equation to solve for x:
7x - 5 = 4(x + 1)
Solving this equation, we get x = 3. Substituting x back into the expression for RS gives us RS = 4(3 + 1), which equals 16. Therefore, the length of RS is 16 meters.