Multiple choice

Two cars are moving with same velocity of $30\ km\ h^{-1}$ maintaining a distance of $5\ km$ between them. Speed of third car moving in the opposite direction and meeting the two cars at an interval of $240\ s$ is

  1. $45 \:km\ h^{-1}$
  2. $30 \:km\ h^{-1}$
  3. $55 \:km\ h^{-1}$
  4. $35 \:km\ h^{-1}$
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A Correct answer
Explanation

Relative speed of third car with respect to the two cars is (V + 30). Distance between cars is 5 km. Time to cover 5 km is 240 s = 240/3600 hr = 1/15 hr. Relative speed = Distance / Time = 5 / (1/15) = 75 km/hr. Since V + 30 = 75, V = 45 km/hr.

AI explanation

The relative speed of the third car with respect to the two oncoming cars is the sum of their individual speeds, since they are moving in opposite directions. The third car covers the 5 km gap between the two cars in 240 seconds, which is 240 divided by 3600 hours, meaning the relative speed is 5 divided by (240/3600), equaling 75 km/h. Subtracting the 30 km/h speed of the oncoming cars from this relative speed gives the third car's actual speed of 45 km/h.

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