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Question Number 206399 by BaliramKumar last updated on 13/Apr/24

Commented by mr W last updated on 14/Apr/24

$s i n c e t h e q u e s t i o n a s k s t h e r a t i o o f$ $‘ ‘ {t h e i r}^{″} s p e e d s, a n s w e r s (b), (c), (d)$ $a r e a l l c o r r e c t .$ $w h e n t h e q u e s t i o n a s k s t h e r a t i o o f$ $t h e s p e e d s o f ‘ ‘ d o g, l i o n a n d {f o x}^{″},$ $t h e n o n l y a n s w e r (c) i s c o r r e c t .$
	Answered by mr W last updated on 13/Apr/24

	$d i s t a n c e c o v e r e d b y e a c h j u m p f r o m$ $d o g, l i o n a n d f o x i s : J_{D}, J_{L}, J_{F}$ $s p e e d o f d o g, l i o n a n d f o x : v_{D}, v_{L}, v_{F}$ $8 J_{D} = 16 J_{L} = 24 J_{F}$ $\Rightarrow J_{D} = 2 J_{L} = 3 J_{F}$ $t = \frac{8 J_{D}}{v_{D}} = \frac{12 J_{L}}{v_{L}} = \frac{15 J_{F}}{v_{F}}$ $\Rightarrow \frac{8 J_{D}}{v_{D}} = \frac{6 J_{D}}{v_{L}} = \frac{5 J_{D}}{v_{F}} \Rightarrow \frac{8}{v_{D}} = \frac{6}{v_{L}} = \frac{5}{v_{F}}$ $\Rightarrow v_{D} : v_{L} : v_{F} = 8 : 6 : 5$ $\Rightarrow a n s w e r (C)$
	Commented by BaliramKumar last updated on 13/Apr/24

	$thanks$
	Answered by A5T last updated on 13/Apr/24

	$D o g, l i o n, f o x d i s t a n c e / j u m p = x, y, z r e s p .$ $\Rightarrow 8 x = 16 y = 24 z \Rightarrow x = 2 y = 3 z$ $D o g, l i o n, f o x t i m e / j u m p = t_{1}, t_{2}, t_{3}$ $8 t_{1} = 12 t_{2} = 15 t_{3} \Rightarrow t_{1} = \frac{3 t_{2}}{2} = \frac{15 t_{3}}{8}$ $\frac{x}{t_{1}} : \frac{y}{t_{2}} : \frac{z}{t_{3}} = \frac{x}{t_{1}} : \frac{\frac{x}{2}}{\frac{2 t_{1}}{3}} : \frac{\frac{z}{3}}{\frac{8 t_{1}}{15}} = \frac{x}{t_{1}} : \frac{3 x}{4 t_{1}} : \frac{5 x}{8 t_{1}} = 8 : 6 : 5$
	Commented by BaliramKumar last updated on 13/Apr/24

	$thanks$
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