Multiple choice

Two identical trains take $3\ sec$ to pass one another when going in the opposite direction but only $2.5\ sec$ if the speed of one is increased by $50 %$. The time one would take to pass the other when going in the same direction at their original speed is

  1. $10\ sec$
  2. $12\ sec$
  3. $15\ sec$
  4. $18\ sec$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let train length be L and speeds be v1, v2. (v1+v2) = 2L/3. If v1 becomes 1.5v1, (1.5v1+v2) = 2L/2.5 = 0.8L. Solving these equations for the same direction case (v1-v2) leads to 15 seconds.

AI explanation

Let the original speeds of the two identical trains be v1 and v2. The distance needed to pass each other in opposite directions is d = 3(v1 + v2). When one train's speed is increased by 50 percent, the new relative speed is v1 + 1.5v2, allowing us to write the equation 3(v1 + v2) = 2.5(v1 + 1.5v2). Simplifying this yields 3v1 + 3v2 = 2.5v1 + 3.75v2, which reduces to 0.5v1 = 0.75v2, meaning v1 = 1.5v2. Substituting this ratio into the original distance equation gives 3(1.5v2 + v2) = 7.5v2. When moving in the same direction, their relative speed is v1 - v2 = 1.5v2 - v2 = 0.5v2. The time to pass each other is the distance divided by the relative speed, 7.5v2 / 0.5v2 = 15 seconds.

Keep practicing — related questions