Multiple choice

The distance between two stations $A$ and $B$ is $60$ km. Two cars start together from $A$ and $B$. If both the cars go in the same direction, they meet after $3$ hours and if they go in the opposite directions, they meet after $30$ minutes. Assuming that car $A$ has greater speed and both the cars have uniform speeds, find their speeds.

  1. $A = 40$ km/hr, $B = 70$ km/hr
  2. $A = 70$ km/hr, $B = 50$ km/hr
  3. $A = 10$ km/hr, $B = 50$ km/hr
  4. $A = 60$ km/hr, $B = 70$ km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be A and B. When moving in the same direction, relative speed is A - B = 60/3 = 20 km/hr. When moving in opposite directions, relative speed is A + B = 60/0.5 = 120 km/hr. Solving the system A - B = 20 and A + B = 120 gives A = 70 km/hr and B = 50 km/hr.

AI explanation

Let the speed of car A be x km/hr and the speed of car B be y km/hr. When moving in the same direction, their relative speed is (x - y) km/hr, giving the equation 3(x - y) = 60 or x - y = 20. When moving in opposite directions, their relative speed is (x + y) km/hr, giving 0.5(x + y) = 60 or x + y = 120. Solving these equations yields x = 70 and y = 50, so car A travels at 70 km/hr and car B travels at 50 km/hr.

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