Multiple choice

Two stations A and B are $90$ km apart and on a highway. A car starts from A and another from B at the same time. If they go in the same direction, they meet after $9$ hours and if they go in opposite directions, they meet after $\displaystyle 1\frac{2}{7}$ hours. Find the speeds of both the cars.

  1. Speed of Car A $=13 km/hr$ and speed of Car B $= 20 km/hr$
  2. Speed of Car A $= 55 km/hr$ and speed of Car B $= 40 km/hr$
  3. Speed of Car A $= 40 km/hr$ and speed of Car B $= 30 km/hr$
  4. Speed of Car A $= 10 km/hr$ and speed of Car B $= 22 km/hr$
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C Correct answer
Explanation

Let speeds be u and v. (u+v) = 90 / (9/7) = 70. (u-v) = 90 / 9 = 10. Adding equations: 2u = 80, u = 40. v = 30.

AI explanation

Let the speeds of the cars be x and y, assuming x is greater than y. When going in the same direction, their relative speed is (x-y) km/hr, so 90 / (x-y) = 9, meaning x-y = 10. When going in opposite directions, their relative speed is (x+y) km/hr, so 90 / (x+y) = 9/7, meaning x+y = 70. Solving the simultaneous equations x-y = 10 and x+y = 70 gives 2x = 80, so x = 40. Substituting x back into the equation yields y = 30, meaning the speed of Car A is 40 km/hr and the speed of Car B is 30 km/hr.

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