Question

A 300 m long train corsses a platform in 39sec. While it corsses a signal pole in 18sec . What is length of platform

Answer 1

Answer :

The length of the platform is 350 meter.

Explanation :

Given that :

A 300 m long train corsses a platform in 39 sec.

It corsses a signal pole in 18 sec.

To Find :

The length of the platform.

Solution :

We know that :

$\bigstar\;\boxed{\sf Speed = \dfrac{Distance}{Time}}}$

So,

$\sf \\ \\\implies Speed = \left(\dfrac{300}{18}\right)m/sec.$

$\sf \\ \\\implies \dfrac{50}{3}m/sec$

$\star\;\textbf{\underline{\underline{Consider as -}}}$

The length of the platform as - 'x metres'

Then,

$\sf\\ \\\implies \left(\dfrac{x+300}{39}\right)\\ \\ \\\implies \dfrac{50}{3}\\ \\ \\\implies 3(x+300)=1950\\ \\ \\\implies x=350m.$

∴ The length of the platform is 350 meter.

$\rule{300}{1.5}$

$\bigstar\;\textbf{\underline{\underline{Extra Information:}}}$

Speed :

The measure of something that how fast or slow is this called Speed.

Acceleration  :

The capacity of the vehicle to gain speed is called its Acceleration.

Velocity :

The speed of something in a given direction is called its Velocity.

Answer 2

$\bold {\huge {Answer :-}}$

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

✦ ✬Given

➛Length of train = 300 m

➛Time taken to cross the platform = 39 sec

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

✦ ✬To find

➛The length of Platform when it cross a signal in 18 sec

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Since we know,

$\huge{\boxed{\boxed{Speed = \frac{Distance}{time}}}}$

$\bold{\Rightarrow\:Speed=\frac{300}{18}}$

$\bold{\Rightarrow\:Speed=\frac{50}{3}\:\:\:m/sec}$

$\bold{→Therefore, \:the\:speed\:of\:train\:is\:\frac{50}{3}\:\:\:m/sec}$

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

⇨ Now let be the length of platform be x

⇨ Therefore the speed when it cross the poles is

$\bold{\Rightarrow\:Speed=\frac{x+300}{39}\:\:\:m/sec}$

→We know that train is travelling in constant speed hence the speed will be same for both cases.

$\bold{\Rightarrow\:\frac{50}{3} =\frac{x+300}{39}\:\:\:m/sec}$

$\bold{\Rightarrow\:50\:\times\:39= 3(x+300)}$

$\bold{\Rightarrow\:x= 350 \:m}$

Hence, the length of platform is 350 m