Final answer:
The correct answer is option (d) Runner 1: 5 m/s, Runner 2: 3 m/s. This is determined through solving a system of equations based on the given conditions of how long it takes for the runners to pass each other both when running in opposite and the same direction.
Step-by-step explanation:
The correct answer is option (d) Runner 1: 5 m/s, Runner 2: 3 m/s.
Let's denote the speed of runner 1 as v1 and the speed of runner 2 as v2. When the runners are moving in opposite directions, their relative speed is (v1 + v2), and they meet in 30 seconds, so the distance they cover together is the perimeter of the track. Hence, (v1 + v2) * 30 = 390 meters.
Similarly, when they are moving in the same direction, their relative speed is (v2 - v1), since the faster has to catch up with the slower, and they meet in 130 seconds. So, (v2 - v1) * 130 = 390 meters.
Now we have two equations:
1) 30v1 + 30v2 = 390
2) 130v2 - 130v1 = 390
Dividing both sides of the equations by 30 and 130 respectively, we get:
v1 + v2 = 13
v2 - v1 = 3
Adding these two equations together cancels out v1 and gives us 2v2 = 16, or v2 = 8/2 = 4 m/s. Subtracting the second equation from the first one gives us 2v1 = 10, or v1 = 10/2 = 5 m/s.
Therefore, runner 1's speed is 5 m/s and runner 2's speed is 3 m/s.