Question

If a 55 m long train crosses a 220 m long platform in 10 sec, then in what time it cross a pole​

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{The length of train} = 55 \: m$

        $\text{The length of platform} = 220 \: m$

$\implies \: \text{Total distance covered by the train} = 220 + 55 = 275 \; m$

        $\text{Time taken by train to cover that distance} = 10 \: s$

        $\text{We know that Speed} = \dfrac{\text{Distance}}{\text{Time}}$

$\implies \:\text{Speed of train} = \dfrac{\text{Total Distance covered}}{\text{Total time taken}}$

$\implies \: \text{Speed of train} = \dfrac{275}{10} = 27.5 \: ms^{-1}$

        $\text{Distance covered by train while crossing pole} = 55 \: m$

        $\text{Speed of train} = 27.5 \: ms^{-1}$

$\implies \: \text{Time taken to cross the pole} = \dfrac{\text{Distance covered}}{\text{Speed of train}}$

$\implies \: \text{Time taken to cross the pole} = \dfrac{55}{27.5}$

$\implies \: \text{Time taken to cross the pole} = \dfrac{550}{275}$

$\implies \: \text{Time taken to cross the pole} = \dfrac{110}{55}$

$\implies \: \text{Time taken to cross the pole} = \dfrac{10}{5}$

$\implies \: \boxed{\boxed{\text{Time taken to cross the pole} = 2 \: seconds}}$