Question

a train crosses a platform 90 long and a man standing on the platform in 15 seconds find the speed of the train
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Answer 1

$speed = \frac{90}{15} = 6$

Answer 2

Question:-

• A train passes a platform 90 m long in 30 seconds and a man standing on the platform in 15 seconds. The speed of the train is?

Answer:-

• $\large\boxed{\underline{{\rm 21.6\:km/hr}}}$

Given:-

• Length of platform = 90 m

• Time taken by the train to cross the platform = 30 sec

• Time taken by the train to pass the platform

To Find:-

• Length of the train = ?

• Speed of the train = ?

Solution :-

Let the speed of the train be x.

Let the length of the train be y.

$\boxed{\underline{\red{\rm \dfrac{Length\:of\:the\:train}{Speed\:of\:the\:train} =Time \:taken\: by\: the\: train\: to \: pass \:the\: man}}}$

$:\implies\:\: \rm{\dfrac{y}{x} = 15}$

$:\implies\:\:\rm{y=15x}\:\:..........(1)$

Now,

$\boxed{\underline{\red{\rm \dfrac{Length\:of\:the\:train+Length \:of\:the\:platform}{Speed\:of\:the\:train} =Time \:taken\: by\: the\: train\: to \: cross \:the\: man}}}$

$:\implies\:\:\rm{\dfrac{y+90}{x} }$

$:\implies\:\:\rm{\dfrac{30}{x} }\:\:............(2)$

Putting the value of y from (1) in (2) :-

$:\implies\:\:\rm{15x+90=30x }$

$:\implies\:\:\rm{15x+90-30x=30x-30x }$

$:\implies\:\:\rm{-15x+90=0 }$

$:\implies\:\:\rm{-15x+90-90=0-90 }$

$:\implies\:\:\rm{-15x=-90 }$

$:\implies\:\:\rm{\dfrac{-15x}{-15} }$

$:\implies\:\:\rm{\dfrac{-90}{-15} }$

$:\implies\:\:\rm{x=6\:sec}$

Speed of the train km/hr :-

$:\implies\:\:\rm{6 \times \dfrac{18}{5} }$

$:\implies\:\:\rm{\dfrac{6}{1} \times \dfrac{18}{5} }$

$:\implies\:\:\rm{\dfrac{6 \times 18}{1 \times 5}}$

$:\implies\:\:\rm{ \dfrac{105}{5} }$

$:\implies\:\:\rm{21.6\: km/hr}$

$\therefore \:\rm{Speed\: of \:the\: train = 21.6\:km/hr}$