Train a and train b leave a central station at the same time. they travel the same speed, but in opposite directions, with train a heading towards station a, and train b heading towards station b. train a reaches station a after 212 h. train b reaches station b after 4 h. station a and station b are 585 mi apart. what is the rate of the trains?

Recall your d  = rt, distance = rate * time

so, keeping in mind that both trains are going at the same speed, say speed of "r" mph, after 212 hours A arrived at station A and after 4 hours, B arrived at station B.

now, the distance covered by train A is say "d", we know both stations are 585 miles apart, so, if train A covered "d" miles in those 212 hours, then train B covered the slack from 585 and d, that is "585 - d".