Question

a train crosses a platform in 60 Seconds at a speed of 40 kilometres per hour how much time will take it to cross an electrical pole if the length of a platform is hundred metres​

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

Given,

Time taken by train to cross the platform, t = 60 seconds

Speed of the train, S = 40 kmph

Length of the Platform = 100 m

time taken by the train to cross an electrical pole = ?




$\underline{\LARGE{\textsf{Step-1:}}}$

$\sf\textsf{Express the Speed of the train in mps}$

$\quad\LARGE{\quad \boxed{\bigstar\; \mathbf{1\: kmph\: =\: \dfrac{5}{18}\: mps\quad}}}$

$\sf\textsf{Multiply with 40 in both sides}$

$\implies \mathsf{40\: kmph = \dfrac{5}{18}\times40\: mps}$

$\implies \mathsf{40\: kmph = \dfrac{200}{18}\: mps}$

$\implies \mathsf{40\: kmph = \dfrac{100}{9}\: mps}$

$\therefore \textsf{Speed of the train = \dfrac{100}{9} mps}$




$\underline{\LARGE{\textsf{Step-2:}}}$

$\sf\textsf{Consider a variable for length of the train}$

$\sf\textsf{Length of the train is not mentioned}\\\sf\textsf{in the given data.}$

$\sf\textsf{Let the length of the train be \textbf{x meters}}$




$\underline{\LARGE{\textsf{Step-3:}}}$

$\sf\textsf{Note the distance covered by the train}\\\sf\textsf{in crossing a platform}$

$\sf\textsf{Distance covered by the train in crossing}\\\sf\textsf{the platform is equal to sum of Lengths of}\\\sf \textsf{train and the platform}$

$\implies \sf\textsf{Distance covered = x+100}$




$\underline{\LARGE{\textsf{Step-4:}}}$

$\sf\textsf{Find the length of the train}$

$\sf\textsf{Given, time taken by the train to cover}\\\sf\textsf{(x+100) m, with a speed of 40 kmph = 60 s}$

$\quad\LARGE{\quad \boxed{\bigstar\; \mathbf{Speed\: =\: \dfrac{Distance\: Covered}{time\: taken}\quad}}}$

$\sf\textsf{Substituting Values}$

$\implies \mathsf{\dfrac{100}{9} = \dfrac{x+100}{60}}$

$\sf\textsf{Cross Multiply}$

$\implies \mathsf{9(x+100) = 100(60)}$

$\implies \mathsf{9x+900 = 6000}$

$\implies \mathsf{9x =6000 - 900}$

$\implies \mathsf{9x=5100}$

$\implies \mathsf{x=\dfrac{5100}{9}}$

$\implies \mathsf{x=\dfrac{1700}{3}}$

$\therefore \mathsf{x= 566.6}$




$\underline{\LARGE{\textsf{Step-5:}}}$

$\sf\textsf{Find the time taken by train to cross the electrical pole}$

$\quad \textbf{time taken = \dfrac{Distance\: covered}{Speed} }$

$\sf\textsf{Assuming that the width of the pole is negligible,}\\\sf\textsf{the time taken by the train in crossing the electrical}\\\sf\textsf{pole is equal to time taken by the train in crossing}\\\sf\textsf{it's own length}$

$\sf\textsf{Substituting Values}$

$\implies \sf\textsf{time taken= \dfrac{\frac{1700}{3}}{\frac{100}{9}} }$

$\implies \sf\textsf{time taken= \dfrac{17\cancel{00}}{3}\times\dfrac{9}{\cancel{100}} }$

$\implies \sf\textsf{time taken= 17 \times 3}$

$\therefore \sf\textsf{time taken = 51 s}$



$\blacksquare\; \; \sf\textsf{time taken by the train to cross}\\\sf\textsf{an electrical pole = \LARGE{\underline{\Large{\textbf{51 Seconds}}}}}$