SOLUTION: Hi I am a math teacher, but I do not understand the following relationship: If two trains start at the same time from points A and B towards each other and after crossing they

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Question 612166: Hi
I am a math teacher, but I do not understand the following relationship:
If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:
(A's speed) : (B's speed) = [sqrt (b) : sqrt (a)]
I can not prove the above formula.
Please help me. Thank you very much.
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
I think there are too many unknowns to make such a relationship.
We don't know the time for A to point X
We don't know the time for B to point Y
The distance from point A to point B is d
d=X+Y
A*x+B*y=d
They meet at point X
x= A's time to point X
y= B's time to point X
Train A goes the whole distance from A to B
A*x+A*a=d
from A to x for x sec then from x to B for a sec
Train B goes the whole distance from B to A
B*y+B*b=d
from B to x for y sec from x to a for b sec