Answer:
The Man needs to run at 9 mph 
Step-by-step explanation:
Let M stand for the man's speed in mph.  When the man  
runs toward point A, the relative speed of the train with respect  
to the man is the train's speed plus the man's speed (45 + M).  
When he runs toward point B, the relative speed of the train is the  
train's speed minus the man's speed (45 - M).
When he runs toward the train the distance he covers is 2 units.  
When he runs in the direction of the train the distance he covers  
is 3 units. We can now write that the ratio of the relative speed  
of the train when he is running toward point A to the relative speed  
of the train when he is running toward point B, is equal to the  
inverse ratio of the two distance units or
               (45 + M)          3
               -----------  =      ---
               (45 - M)          2
           90+2 M=135-3 M
⇒5 M = 45
⇒ M = 9 mph
The Man needs to run at 9 mph