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

Options

A. ` 40 km h^(-1)`
B. 45 km h^(-1)`
C. ` 50 km h^(-1)`
D. ` 35 km h^(-1)`

Answer

B

Explanation

Let car ` C` be moving in opposite direction to (A) and (B) with velocity ` vec_C` relave to ground. Then relative velocity of ` C` relative to ` A` and ` B` will be
` vec v (rel) = vec v _C - vec v`, As ` vec v` is opposite to ` vec v_C` Hence, time taken by car ` C` to cross the cars `A` and
` B` will be ` t= S/v_(rel)` or ` 4 /( 60) = 5/( v_C+30)`
or` v_c = 45 km h^(-1)`.