Hello, zenith20!

Two trains start at the same time, one from B to M and the other from M to B.

If they arrive at their destinations 1 hour and 4 hours resp. after passing each other,

how much faster is one train running than the other?

Train #1 starts at $\displaystyle B$ and moves east at $\displaystyle b$ mph.

In $\displaystyle t$ hours, it has moved $\displaystyle bt$ miles.

Code:

P
B *-------------o---------* M
: - - bt - → : - - - → :
P
B *-------------o---------* M
: ← - - - - - : ← mt - :

Train #2 starts at $\displaystyle M$ and moves west at $\displaystyle m$ mph.

In $\displaystyle t$ hours, it has moved $\displaystyle mt$ miles.

They pass each other at point $\displaystyle P.$

Train #1, at $\displaystyle b$ mph, takes 1 hour to travel the distance $\displaystyle mt$

. . We have: .$\displaystyle (b)(1) \:=\:mt \quad\Rightarrow\quad t \:=\:\dfrac{b}{m}$ .[1]

Train #2, at $\displaystyle m$ mph, takes 4 hours to travel the distance $\displaystyle bt$

. . We have: .$\displaystyle (m)(4) \:=\:bt \quad\Rightarrow\quad t \:=\:\dfrac{4m}{b}$ .[2]

Equate [1] and [2]: .$\displaystyle \dfrac{b}{m} \:=\:\dfrac{4m}{b} \quad\Rightarrow\quad b^2 \:=\:4m^2

$

Therefore: .$\displaystyle b \:=\:2m$ . . . Train #1 is twice as fast as Train #2.