Ratio of Speeds Train Problems Formula || Lesson 2.5 || Aptitude & Reasoning || Learning Monkey

Ratio of Speeds Train Problems Formula
In this class, We discuss Ratio of Speeds Train Problems Formula.
The reader should have prior knowledge of the train problems formula. Click Here.
If two trains are bodies, start simultaneously from points A and B towards each other.
After passing each other, they take b and a second to reach B and A, respectively.
A's speed: B's Speed = √b: √a
The below diagram shows the graphical intuition of the example.
Important: The two trains meet at some point.
The time traveled before the two trains meet t seconds.
The above point helps in solving the formula and helps in solving the bits.
After the two trains met, Train A traveled seconds to reach B.
Train B traveled b seconds to reach A.
Assumption: The speed of the train started at A is 'u' m/s.
The speed of the train started at B is v m/s.
The two trains meet at a point. When the two trains met, they covered the distance from A to B.
Distance from A to B is x.
Distance = speed * Time
x = t (u+v) equation 1
x = (t+a)u equation 2
x = (t+b)v equation 3
Equate 1 and 2 equations.
ut + vt = ut + ua
vt = ua
Equate 1 and 3 equations.
ut + vt = vt + vb
ut = vb
t = vb/u
Substituting we get
v(vb/u) = ua
v^2 b = u^2 a
u/v = √b/√a

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