Final answer:
The problem is a relative motion scenario where a jogger must run with a minimum speed equal to the train's speed of 30 km/h to reach the closest end of the bridge, but this speed is not listed in the provided options, indicating a discrepancy in the question.
"The correct option is approximately option E"
Step-by-step explanation:
The problem presented is a classic relative motion problem that can be resolved using basic algebra. Given that the jogger has completed 3/4 of the distance across the bridge when he sees the train, and he can escape to either end of the bridge just in time, we assume that the time it takes for the jogger to escape to the closest end is the same amount of time it takes the train to reach that end of the bridge. In this scenario, the train covers 1/4 of the bridge's length, while the jogger covers the remaining 1/4 in the same time.
If the jogger runs towards the end of the bridge he is closer to (1/4 the distance), then the speed of the jogger needs to match the train's approach speed over the last 1/4 of the bridge. The train's speed is 30 km/h, so to run the last quarter of the bridge's length, the jogger's speed must be at least 30 km/h as well.
The jogger can also choose to run towards the distant end of the bridge, which is now three times further away (since he is already at the 3/4 mark), therefore, he needs to travel a distance equal to 3/4 the length of the bridge before the train covers 1/4 the length. This means his speed must be at least three times the train's speed divided by four, which is (3/4) * 30 km/h, equating to 22.5 km/h. However, since this is not one of the answer options, we'll have to use the scenario where the jogger runs towards the closest end of the bridge, requiring a minimum speed of 30 km/h to escape the train, which exceeds all the given options. Therefore, this problem seems to have a discrepancy since none of the provided answer choices are correct based on the given information.