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(A) Let the speeds of the cars starting from $A$ and $B$ be $x \, km/h$ and $y \, km/h$ respectively,where $x > y$.Case $I$: When both cars travel in

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(A) Let the speeds of the cars starting from $A$ and $B$ be $x \, km/h$ and $y \, km/h$ respectively,where $x > y$.Case $I$: When both cars travel in the same direction,the relative speed is $(x - y) \, km/h$.Given that they meet in $5 \, hours$ over a distance of $100 \, km$:$5(x - y) = 100 \Rightarrow x - y = 20$ .....$(1)$Case $II$: When both cars travel towards each other,the relative speed is $(x + y) \, km/h$.Given that they meet in $1 \, hour$ over a distance of $100 \, km$:$1(x + y) = 100 \Rightarrow x + y = 100$ .....$(2)$Adding equations $(1)$ and $(2)$:$(x - y) + (x + y) = 20 + 100$$2x = 120 \Rightarrow x = 60 \, km/h$.Substituting $x = 60$ in equation $(2)$:$60 + y = 100 \Rightarrow y = 40 \, km/h$.The speed of the faster car is $60 \, km/h$.

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