Train A and train $B$ are moving toward each other on parallel tracks. On train $A,$ the locomotive blows a whistle continuously. A traveler in train B hears a frequency of $370$ Hz while approaching train A $,$ a frequency of $256$ Hz when exactly parallel with the locomotive of train A and a frequency of $213$ Hz when the trains are moving away from each other.

If the speed of sound in air is $340\frac{m}{s},$ then what are the speeds of the two trains?

$($This is an MCAT problem.$)$