Multiple choice

Two cars are moving in the same direction with the same speed $30km/hr$. They are separated by a distance of $5km$ the speed of a car moving in the opposite direction if it meets these two cars at interval of 4 minutes, will be:

  1. $40km/hr$
  2. $45km/hr$
  3. $30km/hr$
  4. $15km/hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The two cars are 5 km apart, and the opposite-moving car meets them 4 minutes apart, or 1/15 hour. Their relative speed is therefore 5 ÷ (1/15) = 75 km/hr. Since the cars move at 30 km/hr in the opposite direction, the other car's speed is 75 - 30 = 45 km/hr.

AI explanation

Using the concept of relative speed for objects moving in opposite directions, the relative speed is the sum of their speeds. Let the speed of the third car be v km/hr; the relative speed becomes (30 + v) km/hr. The third car covers the 5 km gap at this relative speed in 4 minutes (or 4/60 hours), so we write 5 divided by (30 + v) equals 4/60. Solving this equation gives 75 equals 30 + v, so the speed of the car is 45 km/hr.

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