Multiple choice

The distance between two towns is $300$ km. Car $A$ and Car $B$ starts simultaneously from these towns and move towards each other. The speed of Car $A$ is more than that of Car $B$ by $7$ km/h. If the distance between the cars after two hours is $34$ km. Find the speed of both cars.

  1. Speed of car $B$ is $63$ km/h and speed of car $A$ is $70$ km/h
  2. Speed of car $B$ is $70$ km/h and speed of car $A$ is $75$ km/h
  3. Speed of car $B$ is $50$ km/h and speed of car $A$ is $65$ km/h
  4. Speed of car $B$ is $72$ km/h and speed of car $A$ is $80$ km/h
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A Correct answer
Explanation

Let speed of B be v. Speed of A is v + 7. Relative speed = 2v + 7. Distance covered in 2 hours = 2 * (2v + 7) = 4v + 14. Remaining distance = 300 - (4v + 14) = 34. 286 - 4v = 34, so 4v = 252, v = 63. Speed of A = 63 + 7 = 70.

AI explanation

In two hours, the two cars cover a combined distance of 300 - 34 = 266 km. Using the formula Speed = Distance / Time, their combined relative speed is 266 / 2 = 133 km/h. Let the speed of Car B be s, so the speed of Car A is s + 7. Setting up the equation s + (s + 7) = 133, we get 2s = 126. Solving this gives the speed of Car B as 63 km/h and the speed of Car A as 70 km/h.

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