Multiple choice

Points $A$ and $B$ on a national highway are at a distance of $120 km$ from each other. One car starts from $A$ and another from $B$ at the same time. The car which starts from $A$ moves with a constant speed along the direction $AB$ and the second moves with a constant speed in the same direction from $B$. The first car overtakes the second car in $4$ hours. However, if the second car moves from $B$ towards $A$ then the two meet each other after $2$ hours. Find the speed of the car which starts from $A$.

  1. $45 {km}/{hr}$
  2. $65 {km}/{hr}$
  3. $85 {km}/{hr}$

  4. None of these
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A Correct answer
Explanation

Let speeds be v1 and v2. Case 1 (same direction): 120 = (v1 - v2) * 4 => v1 - v2 = 30. Case 2 (opposite direction): 120 = (v1 + v2) * 2 => v1 + v2 = 60. Adding the equations: 2*v1 = 90 => v1 = 45 km/hr.

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 move in the same direction, the relative speed is x - y, giving the equation 4(x - y) = 120. When they move in opposite directions, the relative speed is x + y, giving the equation 2(x + y) = 120. Solving these simultaneous equations yields x - y = 30 and x + y = 60. Adding both equations gives 2x = 90, so x = 45 km/hr. The result is 45 km/hr.

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