Question

Two trains travel in opposite directions at 40 kmph and 50 kmph and a man sitting in slower train observes the faster train pass him completely in 10 seconds The length of the faster train is:​

Answer 1

❈ AnSwer :

• Length of the fastest train is 917m.

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❈ GiVen :

It is provided that the trains travel in opposite directions with 40 km/h and 50 km/h respectively and a man is sitting in the slower train and he observes that the faster train passes within 10 seconds.

❈ To Find :

• We need to find the length of the faster train.

❈ SoluTion :

As the trains travel in opposite direction here,

We need to find its relative speed.

So,

★Relative speed=(50+40)km/hr

⠀⠀⠀⠀⠀⠀⠀⠀⠀=(90+5/18)m/sec

⠀⠀⠀⠀⠀⠀⠀⠀⠀=(1625/18)m/sec

★ Length of the fastest train :

= 1625/18 × 10

=917m(approx.)

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Answer 2

Solution :

$\bigstar$ Two train travel in opposite direction's at 40 km/hrs & 50 km/hrs.

A man observes the faster train pass in completely in 10 sec.

$\underline{\boldsymbol{According\:to\:the\:question\::}}}$

Let the length of the faster train be r m

Firstly, we get given units convert into m/sec.

$\boxed{\begin{minipage}{4cm} \sf We know that; \\ 1 km = 1000 m\\ \sf 1 hour = 60 \times \:\sf 60\: seconds .\\\\\therefore 1m/sec.=\cancel{\dfrac{1000}{3600} }\\\\\sf 1m/sec.= \dfrac{5}{18} \end{minipage}}$

$\underline{\mathcal{RELATIVE\:SPEED\::}}$

$\mapsto\sf{First\:train\:speed + Second\:train\:speed}\\\\\mapsto\sf{(40+50)km/hrs}\\\\\mapsto\sf{\bigg(\cancel{90}\times \dfrac{5}{\cancel{18}} \bigg)m/sec.}\\\\\mapsto\sf{(5\times 5)m/sec.}\\\\\mapsto\bf{25m/sec.}$

Now;

We know that formula of the time :

$\boxed{\bf{Time=\frac{Distance}{Speed} }}}$

$\longrightarrow\sf{10=\dfrac{r}{25m} }\\\\\\\longrightarrow\sf{r=(25\times 10 )\:m}\\\\\longrightarrow\bf{r=250\:m}$

Thus;

The length of the faster train is 250 m .