Places A and B are 90, km apart from each oth | vedclass

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Question

(A) Let the speed of the car starting from $A$ be $x\, km/hr$ and the speed of the car starting from $B$ be $y\, km/hr$.When moving in the same direct

Vedclass · Accepted Answer

$40\, km/hr, 30\, km/hr$

Vedclass · Answer

(A) Let the speed of the car starting from $A$ be $x\, km/hr$ and the speed of the car starting from $B$ be $y\, km/hr$.When moving in the same direction,the relative speed is $(x - y)\, km/hr$. Since they meet in $9$ hours,the distance covered is $9(x - y) = 90$,which simplifies to $x - y = 10$ (Equation $1$).When moving in opposite directions,the relative speed is $(x + y)\, km/hr$. Since they meet in $\frac{9}{7}$ hours,the distance covered is $\frac{9}{7}(x + y) = 90$,which simplifies to $x + y = 70$ (Equation $2$).Adding Equation $1$ and Equation $2$: $(x - y) + (x + y) = 10 + 70$,so $2x = 80$,which gives $x = 40\, km/hr$.Substituting $x = 40$ into Equation $1$: $40 - y = 10$,so $y = 30\, km/hr$.Thus,the speeds of the cars are $40\, km/hr$ and $30\, km/hr$.

Places $A$ and $B$ are $90\, km$ apart from each other on a highway. $A$ car starts from $A$ and another from $B$ at the same time. If they move in the same direction,they meet in $9$ hours and if they move in opposite directions,they meet in $\frac{9}{7}$ hours. Find the speeds of the cars.

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