Two cars are travelling in the same direction with a velocity of 60 km per hour. they are separated by a distance of 5 km. a truck moving in opposite direction meets the two cars in a time interval of 3 minute. the velocity of the truck in kilometre per hour is ?

Basics first :

1. If two objects move in same direction, their relative speed will be the difference of their individual speeds.
2. If two objects move in opposite direction, their relative speed will be the sum of their individual speeds.
3. Distance = Speed x Time

=> If two cars are moving in same direction at same speed of 30 kmph, then relative speed is ZERO. That means, the 5km distance between them will always remain constant.

Now, if a third truck travels in the opposite direction at a speed of “s”, then relative speed is s + 30.

Since it meets the two cars at an interval of 3 minutes, it means it covers a distance of 5kms in 3 minutes or 3/60 = 1/20 hours at a relative speed of “s + 30”.

=> 5 = (s + 30) x 1/20

=> s + 30 = 100

=> s = 70 kmph

This Speed is Relative to a Frame of Reference attached to one of the two moving cars (which are moving with constant velocity of 30kmph).

For a Frame of Reference attached to the Ground,

S = 45+30 = 75 Kmph.