logic problem?

Question

A genius was walking along a railroad track when she came upon a narrow railroad bride.
The bridge was only wide enough to allow the train to pass.
When she was 3/8 of the way across, she heard a train whistle. Being a genius, she instantly realized that if she ran back to the beginning of the bridge at her speed, she would be able to get out of the way just in time to avoid being hit by the train and if she were to continue at her speed to the end of the bridge, she would just have time to get off the bridge before being hit by the train.
If she runs at 10.5mph, how fast is the train going?

Answer 1

the train was going fast enough to trample her *** over

Answer 2

1) Let V equal the speed of the runner = 10.5 mph

2) Let U equal the speed of the train.

Assertion: U / V = 4

Proof:

3) First, the time it takes the train to get to the end of the bridge equal the time it takes the runner to get to the end of the bridge
( X + L ) / U = ( L - K ) / V

where
L = The length of the bridge
X = The distance from the train, to the bridge entrance, when the whistle blew.
K = The distance from the bridge entrance to the runner, when the whistle blew. K = 3L / 8

4) Second, the time it takes the train to get to the start of the bridge equal the time it takes the runner to get back to the start of the bridge
X / U = K / V

5) Deviding 3) by K
( X / K ) + ( L / K ) = ( U / V ) * ( ( L / K ) - 1 )

6) Solving 4) and 5) gives U / V = 4