If train a is going 50 mph and train b is going 30 mph, train a starts 500 miles away from train b, and they are traveling in opposing directions, at what point will train b reach train a?

   after 6 hours 15 minutes, they will meet at a point 187.5 miles from train B's start

Step-by-step explanation:

Assuming the trains are traveling toward each other, they are closing the gap at the rate of 50+30 = 80 miles per hour. Then there will be no gap left after ...

  (500 mi)/(80 mi/h) = 25/4 h = 6.25 h . . . time until trains meet

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In that time, Train A will have traveled ...

  (50 mi/h)(6.25 h) = 312.5 mi . . . . distance from A's start

and Train B will have traveled ...

  (30 mi/h)(6.25 h) = 187.5 mi . . . . distance from B's start

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The B will reach A at a point 3/8 of the distance from B to A, 187.5 mi from B's start.