1. ## "Two Trains"

"Two Trains"
Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

could anybody help me find the correct answer (with detaied solution please)

2. 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 $B$ and moves east at $b$ mph.
In $t$ hours, it has moved $bt$ miles.

Code:
                    P
B *-------------o---------* M
: - - bt  - → : - - - → :

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

Train #2 starts at $M$ and moves west at $m$ mph.
In $t$ hours, it has moved $mt$ miles.

They pass each other at point $P.$

Train #1, at $b$ mph, takes 1 hour to travel the distance $mt$
. . We have: . $(b)(1) \:=\:mt \quad\Rightarrow\quad t \:=\:\dfrac{b}{m}$ .[1]

Train #2, at $m$ mph, takes 4 hours to travel the distance $bt$
. . We have: . $(m)(4) \:=\:bt \quad\Rightarrow\quad t \:=\:\dfrac{4m}{b}$ .[2]

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

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

3. Thanks a Million to our beloved Soroban

you're always there to help