Question

a train 420 m long is running at a speed of 90 km/hr. if it crosses a platform in 45 second. I find the length of the platform ​

Answer 1

First of all we will convert the speed to m/s

To convert to m/s, multiply with 5/18

90 km/hr = 90 × 5/18 m/s

→ 25 m/s

Now given that it crosses the platform in 45 seconds. Let the length of platform be x

So, total distance travelled by train = Length of platform + Length of train

= x + 420 m

Time = 45 seconds

Speed = 25 m/s

we know that, speed = distance/time

So, substitute the values of speed, distance and time

→ 25 = (x + 420)/45

→ x + 420 = 45 × 25

(By cross multiplication)

→ x + 420 = 1125

→ x = 1125 - 420

→ x = 705 m

Hence, the length of the platform is 705 m

$\rule{200}{2}$

Answer 2

$\mathfrak{Answer:}$

= 705 m.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\bold{Given\:in\:the\:Question:}}$

• Length of the train = 420 m.
• Time taken to cross the plateform = 45 sec.

• Speed of the train :

$\tt{=90\:km\:h^{-1}}\\\\\\\tt{=90\times\dfrac{5}{18}\;m\;s^{-1}}\\\\\\\tt{=5\times 5\;m\;s^{-1}}\\\\\\\tt{=25\;m\;s^{-1}.}$

Let the length of the plateform be x meter.

$\boxed{\bold{Time\;to\;cross\;plateform=\dfrac{Length\;of\;train+Length\;of\;plateform}{Speed\;of\;train}}}\\\\\\\mathfrak{According\;to\;Question:}$

$\implies\tt{45=\dfrac{420+x}{25}}\\\\\\\implies\tt{420+x=45\times 25}\\\\\\\implies\tt{420+x=1125}\\\\\\\implies\tt{x=1125-420}\\\\\\\implies\tt{x=705.}\\\\\\\boxed{\boxed{\bold{Length\;of\;Plateform=705\;m.}}}$