Question

A train covers a distance of 600 km at x km/hr. Had the speed been (x + 20) kmhr, the time taken to cover the same distance would have been reduced by 5 hours. Write down an equation in x and solve it to evaluate x.​

Answer 1

$\boxed {\boxed{ { \green{ \bold{ \underline{Verified \: Answer \: }}}}}}$

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$\bigstar{\underline{\underline{{\sf\ \red{ SOLUTION:-}}}}}$

according to the question,

$\frac{600}{x} - \frac{600}{x + 20} = 5 \\ \frac{600x + 12000 - 600x}{ {x}^{2} + 20x } = 5 \\ 600x + 12000 - 600x = 5 {x}^{2} + 10x \\ {5x}^{2} + 100x - 12000 = 0 \\ {x}^{2} + 20x - 2400 = 0 \\ {x}^{2} + 60x - 40x - 2400 = 0 \\ x(x + 60) - 40(x + 60) = 0 \\ (x + 60)(x - 40) = 0 \\ x - 40km/hr  \: since \: speed \: cannot \: be negative$

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Answer 2

$\huge\sf{\underline{\underline{\underline{\blue{Answer}}}}}$

$\sf{\underline{According \: to \: question,}}$

$\sf{\frac{600}{x} - \frac{600}{x + 20} = 5}$

$\implies\sf{ \frac{600x + 12000 - 600x}{ {x}^{2} + 20x} = 5}$

$\implies\sf{600x+12000-600x = {5x}^{2} + 10x}$

$\implies\sf{ {5x}^{2} + 100x - 12000 = 0}$

$\implies\sf{ {x}^{2} + 20x - 2400 = 0}$

$\implies\sf{ {x}^{2} + 60x - 40x - 2400 = 0}$

$\implies\sf{x(x + 60) - 40(x + 60)}$

$\implies\sf{(x + 60)(x - 40)}$

$\sf{x-40 \: km/hr \: since \: speed \: can't \: be \: negative.}$