Answer:
The Man needs to run at 9 mph
Step-by-step explanation:
Let M stand for the man's speed in mph. Â When the man Â
runs toward point A, the relative speed of the train with respect Â
to the man is the train's speed plus the man's speed (45 + M). Â
When he runs toward point B, the relative speed of the train is the Â
train's speed minus the man's speed (45 - M).
When he runs toward the train the distance he covers is 2 units. Â
When he runs in the direction of the train the distance he covers Â
is 3 units. We can now write that the ratio of the relative speed Â
of the train when he is running toward point A to the relative speed Â
of the train when he is running toward point B, is equal to the Â
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
Answer: 9 mph
Step-by-step explanation:
Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .
If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5
The remaining distance = 1 - 4/5 = 1/5
If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be
Speed = distance/time
Time = 1/5d ÷ speed
The time it will take the train to cover the entire distance d will be
Time = d ÷ 45
Equate the two time
1/5d ÷ speed = d ÷ 45
Speed = d/5 × 45/d
Speed = 9 mph
