Question

Two trains A and B, 100m and 60m long, are moving in opposite directions on parallel tracks. The velocity of the shorter train is 3 times that of the longer one. If the trains take 4s to cross each other, the velocities of the trains are​

Answer 1

total distance to cross 160 m

let vel of longer train be v

vel of shorter train is 3v

relative vel = 4v

time = 160/4v = 4

v = 10 m/s

3v = 30 m/s

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Length of train "A" = 100m.

Length of train "B" = 60 m.

Velocity of Longer train = v.

Velocity of Shorter train = 3v.

$\huge{\bold{\underline{Explanation:-}}}$

Total distance to be covered = 100 + 60

${ \therefore}$ Distance = 160 m.

As the trains are moving in opposite direction the relative velocity will be increased.

${v_{ab} = v_a + v_b}$

${v_{ab} = v + 3v}$

${v_{ab} = 4v}$

Relative velocity is 4v.

Now, applying Speed formula.

$\large{\bold{\boxed{\boxed{Speed = \frac{Total \: Distance \: Travelled}{Total \: time \: taken}}}}}$

Substituting the values.

$\large{4v = \frac{160}{4}}$

$\large{ \to 4v = 40 }$

$\large{ \therefore v = 10 m/s}$

Velocities of trains.

Velocity of Longer train (Train "A")= v = 10 m/s

Velocity of Shorter train(Train "B")= 3v = 3 × 10 = 30 m/s.