Two trains run in opposite directions on a circular track. Train Q travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?	Choices: A) 3 B) 6 C) 9 D) 18 E) 22
I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.   My solution is as follows, and I ask anyone to correct me if I am wrong.   Solution 1   Let the distance covered by train Q be X, thus that covered by the train B will be 12*3.14-X   dQ = X dB = 12*3.14 - X   Times taken by A and B are   tQ= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)   Since they have been traveling for the same period of time, then   X/4*3.14 = (12*3.14 - X)/6*3.14   X/2 =(12*3.14 -X)/3   3X = 2(12*3.14 -X)   5X = 24*3.14   X = 24*3.14/5   Plugging that in either equation of (ii) yields t = 6/5   Solution 2   We add the speed of Q and B: totalSpeed = 4*3.14 + 6*3.14 = 10*3.14   Total distance covered = 12*3.14   t ime = distance / speed = 12*3.14/10*3.14 = 6/5.   tQ =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5.
<result>B</result>
Two trains run in opposite directions on a circular track. Train Q travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?