Question

solve this question by full methods please ​

Answer 1

Answer:

Hope it will helpful for u

thanks

Answer 2

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large{\rm{\underline{\underline{Given}}}}$:-

$\rm{ratio \: \: of \: \: the \: \: speeds \: \: of \: \: three \: \: cars \: -}$

$\: \: \: \: \rm{S\displaystyle_{1} \: : \: S\displaystyle_{2} \: : \: S\displaystyle_{3} \: \: = \: \: 1 \: \: : \: \: 3 \: \: : \: \: 5}$

$\large{\rm{\underline{\underline{To \: Find}}}}$:-

$\rm{ratio \: \: among \: \: the \: \: time \: \: taken \: \: by \: \: these \: \: three \: \: cars \: ?}$

$\large{\rm{\underline{\underline{Solution}}}}$:-

we know that -

$\: \: \: \: \: \: \: \: \: \rm{\boxed{\green{\rm{ \: speed \: \: = \: \: \dfrac{Distance}{Time} \: }}}}$

we can say that -

$\hookrightarrow$$\: \: \: \: \: \: \: \: \: \rm{Speed \: \: \propto \: \: \dfrac{1}{Time} }$

So -

ratio of the time taken by these cars -

$\: \: \rm{T\displaystyle_{1} \: : \: T\displaystyle_{2} \: : \: T\displaystyle_{3} \: \: = \: \: \dfrac{1}{S\displaystyle_{1}} \: \: : \: \: \dfrac{1}{S\displaystyle_{2}} \: \: : \: \: \dfrac{1}{S\displaystyle_{3}}}$

$\: \: \rm{T\displaystyle_{1} \: : \: T\displaystyle_{2} \: : \: T\displaystyle_{3} \: \: = \: \: \dfrac{1}{1} \: \: : \: \: \dfrac{1}{3} \: \: : \: \: \dfrac{1}{5}}$

$\: \: \rm{T\displaystyle_{1} \: : \: T\displaystyle_{2} \: : \: T\displaystyle_{3} \: \: = \: \: \dfrac{1}{1} \: \times \: 15 \: \: : \: \: \dfrac{1}{3} \: \times \: 15 \: \: : \: \: \dfrac{1}{5} \: \times \: 15}$

$\: \rm{\boxed{\purple{\rm{ \: T\displaystyle_{1} \: : \: T\displaystyle_{2} \: : \: T\displaystyle_{3} \: \: = \: \: 15 \: \: : \: \: 5 \: \: : \: \: 3 \: }}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━