Multiple choice

Point $A$ and $B$ are $70\ km$ apart on a highway. A car starts from $A$ and another car starts from $B$ at the same time. If they travel in the same direction, they meet in $7$ hours, but if they travel towards each other they meet in one hour. What are their speeds?

  1. $30\ km/hr$ and $40\ km/hr$
  2. $36\ km/hr$ and $40\ km/hr$
  3. $19\ km/hr$ and $20\ km/hr$
  4. $40\ km/hr$ and $50\ km/hr$
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A Correct answer
Explanation

Let speeds be x and y. Same direction: 7(x-y) = 70 => x-y = 10. Opposite direction: 1(x+y) = 70 => x+y = 70. Adding equations: 2x = 80 => x = 40. Then y = 30.

AI explanation

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 they travel in the same direction, their relative speed is x - y, giving the equation 7(x - y) = 70. When they travel towards each other, their relative speed is x + y, giving the equation 1(x + y) = 70. Solving the simultaneous equations x - y = 10 and x + y = 70 yields x = 40 and y = 30, meaning their speeds are 40 km/hr and 30 km/hr.

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