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Question Number 168264 by Mastermind last updated on 07/Apr/22

Answered by som(math1967) last updated on 07/Apr/22

let speed =xkm/hr  ∴((240)/(x−4)) −((240)/x)=2  ⇒240{((x−x+4)/(x(x−4)))}=2  ⇒((240×4)/(x^2 −4x))=2  ⇒x^2 −4x−480=0  ⇒x^2 −24x+20x−480=0  ⇒(x−24)(x+20)=0   x=24   speed=24km/hr

$${let}\:{speed}\:={xkm}/{hr} \\ $$$$\therefore\frac{\mathrm{240}}{{x}−\mathrm{4}}\:−\frac{\mathrm{240}}{{x}}=\mathrm{2} \\ $$$$\Rightarrow\mathrm{240}\left\{\frac{{x}−{x}+\mathrm{4}}{{x}\left({x}−\mathrm{4}\right)}\right\}=\mathrm{2} \\ $$$$\Rightarrow\frac{\mathrm{240}×\mathrm{4}}{{x}^{\mathrm{2}} −\mathrm{4}{x}}=\mathrm{2} \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{480}=\mathrm{0} \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{24}{x}+\mathrm{20}{x}−\mathrm{480}=\mathrm{0} \\ $$$$\Rightarrow\left({x}−\mathrm{24}\right)\left({x}+\mathrm{20}\right)=\mathrm{0} \\ $$$$\:{x}=\mathrm{24}\: \\ $$$${speed}=\mathrm{24}{km}/{hr} \\ $$

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