Multiple choice

Places $P_1$ and $P_2$ are $250$ km apart from each other on a national highway. A car starts from $P_1$ and another from $P_2$ at the same time. If they go in the same direction then they meet in $5$ hours and if they go in opposite directions they meet in $\displaystyle \frac{25}{13}$ hours. The speed of the cars are __________.

  1. $90$ km/hr, $40$ km/hr
  2. $40$ km/hr, $80$ km/hr
  3. $20$ km/hr, $60$ km/hr
  4. $50$ km/hr, $12$ km/hr
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A Correct answer
Explanation

Let speeds be u and v. Same direction: (u-v) = 250/5 = 50. Opposite direction: (u+v) = 250 / (25/13) = 250 * 13 / 25 = 130. Adding equations: 2u = 180, u = 90. Then v = 40.

AI explanation

Let the speeds of the two cars be x km/hr and y km/hr where x > y. When moving in the same direction, their relative speed is x - y, which equals 250 / 5 = 50 km/hr. When moving in opposite directions, their relative speed is x + y, which equals 250 / (25/13) = 130 km/hr. Solving the simultaneous equations x - y = 50 and x + y = 130 yields x = 90 km/hr and y = 40 km/hr. The result is 90 km/hr, 40 km/hr.

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