Final answer:
In order to find the total distance Amy traveled, we can set up an equation using the distances, rates, and times for her outbound and return trips. Solving the equation, we find that the total distance Amy traveled is approximately 225 miles. So, the option A is correct.
Step-by-step explanation:
In order to determine the overall distance Amy covered on her round trip, we must compute the individual distances for her outbound and return journeys.
Employing the formula Distance = Rate × Time, denote the distance to her friend's house as D1 and the return distance as D2, with corresponding times T1 and T2.
Utilizing the speed equation (Speed = Distance / Time), we express T1 = D1 / 45 (outbound trip time) and T2 = D2 / 50 (return trip time). Given that the total driving time is four hours, the equation T1 + T2 = 4 arises.
Substituting the expressions for T1 and T2 yields (D1 / 45) + (D2 / 50) = 4.
To eliminate fractions, we multiply by 2250 (the least common multiple of 45 and 50), resulting in the equation 50D1 + 45D2 = 9000.
As Amy travels the same distance to and from her friend's house (D1 = D2), the equation simplifies to 95D = 9000.
Solving for D, we find D ≈ 225 miles, signifying the total distance Amy traversed.
Therefore, the option A is correct, Amy traveled is approximately 225 miles.