Final answer:
The algebraic equation based on relative speeds indicates that the southbound train travels at 56 mph and the northbound train at 66 mph. However, this does not match any of the provided options, suggesting an error in the question or options.
Step-by-step explanation:
The question involves resolving a problem using algebra and concepts of relative speed. Since the trains are traveling in opposite directions, we add their speeds together to find the total relative speed at which they are moving apart. Let's denote the speed of the southbound train as s mph. Thus, the speed of the northbound train will be s + 10 mph. After 1.5 hours, they are 183 miles apart, so the combined distance covered by both trains is 183 miles.
We can write the equation:
- Total Distance = (Speed of Southbound Train + Speed of Northbound Train) × Time
- 183 = (s + s + 10) × 1.5
Solving this equation:
- 183 = (2s + 10) × 1.5
- 183 = 3s + 15
- 168 = 3s
- s = 56 mph
Therefore, the southbound train is traveling at 56 mph and the northbound train is traveling at 56 mph + 10 mph = 66 mph.
However, this answer does not match any of the provided options, indicating a possible error in the question or the options given. It is important to clarify the question with the student or check for any errors.