Two cars are moving in the same direction with the same speed `30 km //h^(-1)` . They are separated by a distance of 4 km. What is the speed of a car moving in the opposite driection if it meets these two card at an interval if ` 5 mimutes.

Explanation

As the two cars (say A and B) are moving with same velocity, the relative velocity of one (say B) with respect to the other A,
`vec(v)_(BA) = vec(v)_(B) - vec(v)_(A) = v - v = 0`
So, the relative separation between them (= 5 km) always remains the same
Now if the velocity of the car (say C), moving in opposite direction to A and B, is `vec(v)_(C)` releative to ground, then the velocity of car C relative to A and B will be
`vec(v)_("rel") = vec(v)_(C) - vec(v)`
But as `vec(v)` is opposite to `v_(C)`
`v_("rel") = v_(C) - (-30) = (v_(C) + 30) km//hr`
So, the time taken by it to cross the cars A and B, `t = (d)/(v_("rel"))`
or `(4)/(60) = (5)/((v_(C) + 30))` [as 4 minute `= (4)/(60) hr`]
or `v_(C) = 45 km//hr`