Question

If the train travelled 5 km an hour faster
it would take one hour less to travel
210km, what time does it take​

Answer 1

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

${\sf{☞ \ Distance \ travelled \ by \ train \ = \ 210km}}$

$\Large{\green{\tt{\underline{\underline{To \ find \ :-}}}}}$

${\tt{\bold{• \ Original \ speed \ of \ train.}}}$

$\Large{\purple{\tt{\underline{\underline{Formula \ used \ :-}}}}}$

${\sf{↣ \ Time \: = \: \frac{Distance}{Speed}}}$

and

${\sf{↣ \ Distance \: = \: Speed \: \times \: Time}}$

$\Large{\orange{\tt{\underline{\underline{Solution \ :-}}}}}$

${\tt{Let \ the \ original \ speed \ of \ train \ be \ x \ km/hr}}$

${\sf{↣ \ Distance \ travelled \ = \ 210 \ km}}$

${\sf{↣ \ Time \: taken \: = \: \frac{Distance}{Speed} = \frac{210}{x} hr}}$

${\bf{\large{Now, \ according \ to \ question}}}$

${\tt{If \ speed \ is \ increased \ by \ 5km/hr \ it \ will}} \\ {\tt{ take \ 1hr \ less \ than \ usual.}}$

${\sf{↣ \ New \ speed \ of \ train \ = \ x+5 \ km/hr }}$

${\sf{↣ \ Time \ taken \ = \ \frac{210}{x} \ -1}}$

${\tt{Since \ the \ distance \ travelled \ is \ same}}$

${\sf{Distance \ = \ Speed × Time}}$

${\sf{⟹ \ 210 = (x + 5) \times ( \frac{210}{x} - 1)}}$

${\sf{⟹ \ 210 = (x + 5) \times ( \frac{210 - x}{x} )}}$

${\sf{⟹ \ \frac{210}{x + 5} = \frac{210 - x}{x}}}$

${\sf{⟹ \ 210x = (210 - x)(x + 5)}}$

${\sf{⟹ \ 210x = 210x - {x}^{2} + 1050 - 5x}}$

${\sf{⟹ \ 0 = 210x - 210x - {x}^{2} + 1050 - 5x}}$

${\sf{⟹ \ 0 = - {x}^{2} + 1050 - 5x}}$

${\sf{⟹ \ 0 = - 1( {x}^{2} + 5x - 1050)}}$

${\sf{⟹ \ 0 = {x}^{2} + 5x - 1050}}$

Since this is a quadratic equation

${\sf{⟹ \ {x}^{2} + 5x - 1050 = 0}}$

${\sf{⟹ \ {x}^{2} + 35x - 30x - 1050 = 0}}$

${\sf{⟹ \ x(x + 35) - 30(x + 35) = 0}}$

${\sf{⟹ \ (x - 30)(x + 35) = 0}}$

${\sf{⟹ \ x = 30 \: or \: - 35}}$

${\tt{Since \ the \ speed \ cannot \ be \ negative }}\\ {\tt{, neglect \ 35 \ and \ the \ original \ speed}} \\ {\tt{of \ train \ is \ 30km/hr}}$

${\bf{\boxed{ x \ = \ 30km/hr}}}$

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