Final answer:
To find the time for two trains traveling in opposite directions to be 500 km apart, add their speeds to get the relative speed (125 km/h) and divide the distance (500 km) by this speed to get 4 hours.
Step-by-step explanation:
The student's question pertains to a classic problem in kinematics, specifically relative motion. According to the given scenario, one train travels north at 55 km/h, and another travels south at 70 km/h. To determine when they will be 500 km apart, we need to consider their combined relative speed.
The relative speed of the two trains moving in opposite directions is the sum of their individual speeds: 55 km/h + 70 km/h = 125 km/h. To find the time it takes for the trains to be 500 km apart, we can use the formula distance = speed × time. Rearranging the formula to solve for time gives us time = distance / speed. Substituting the known values, we get time = 500 km / 125 km/h.
Therefore, time = 4 hours. It will take 4 hours for the trains to be 500 km apart.