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/hr
B. 45 km/hr
C. 30 km/hr
D. 15 km/hr

Answer

B

Explanation

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, `vecv_(BA)=vecv_B-vecv_A`=v-v=0
So the relative separation between them (=5 km) always remains the same.
Now if the velocity of car (say C) moving in opposite direction to A and B, is `vecv_c` relative to ground then the velocity of car C relative to A and B will be `vecv_"rel."=vecv_c=vecv`
But as `vecv` is opposite to `v_c`.
So `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." rArr 4/60=5/(v_c+30) rArr v_c`= 45 km/hr