Question

a passenger train of length 60m travels at a speed of 80km/h . Another freight train of length 120m travels at a speed of 30 km/h .The ratio of times taken by the passenger train to completely cross the freight train when they are moving in the small direction,and in the opposite direction is​

Answer 1

Answer:

t₁ : t₂ :: 11 : 5

Explanation:

Distance to be covered = (Total length of freight train) + (It's own length too) = 120 + 60 m = 180 meter

When they are going in same direction:

Relative velocity of passenger train = 80 - 30 = 50 km/h

When they are going in opposite direction:

Relative velocity of passenger train = 80 + 30 = 110 km/h

Since,

$velocity=\frac{distance}{time}\\\\time=\frac{distance}{velocity}$

Hence, Ratio of time taken in first and second condition:

$\frac{t_1}{t_2}=\frac{\frac{180}{50}}{\frac{180}{110}}=\frac{110}{50}\\\\t_1:t_2::11:5$

Answer 2

Distance to be covered = (Total length of freight train) + (It's own length too) = 120 + 60 m = 180 meter

When they are going in same direction:

Relative velocity of passenger train = 80 - 30 = 50 km/h

When they are going in opposite direction:

Relative velocity of passenger train = 80 + 30 = 110 km/h

Since,

\begin{lgathered}velocity=\frac{distance}{time}\\\\time=\frac{distance}{velocity}\end{lgathered}

velocity=

time

distance

time=

velocity

distance

Hence, Ratio of time taken in first and second condition:

\begin{lgathered}\frac{t_1}{t_2}=\frac{\frac{180}{50}}{\frac{180}{110}}=\frac{110}{50}\\\\t_1:t_2::11:5\end{lgathered}

t

2

t

1

=

110

180

50

180

=

50

110

t

1

:t

2

::11:5