Question

# Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time at 8:10 AM. If the speeds of the cars are 50 km per hour and 30 km per hour respectively, they will meet each other at${\text{A}}{\text{. 10:10 AM}} \\ {\text{B}}{\text{. 10:30 AM}} \\ {\text{C}}{\text{. 11:10 AM}} \\ {\text{D}}{\text{. 11:20 AM}} \\$

Hint: Here, we will proceed by finding out the relative speed between the two cars and then using the formula i.e., Time taken$= \dfrac{{{\text{Distance travelled}}}}{{{\text{Speed}}}}$ to determine after how many hours these cars will meet each other.

Given, Distance between the two cars d=160 km
Starting time for both the cars when they left their respective initial positions A and B is 8:10 AM
Speed of the first car, x=50 km per hour
Speed of the second car, y=30 km per hour
In order to obtain the relative speed between these two cars which are moving towards each other (i.e., in opposite directions), the individual speeds of these cars will be added.
So, the relative speed between the two given cars, r= x+y=50+30=80 km per hour
As we know that, Time taken$= \dfrac{{{\text{Distance travelled}}}}{{{\text{Speed}}}}$
So, time when both the cars will meet=$\dfrac{{{\text{Initial distance between both the cars}}}}{{{\text{Relative speed between the cars}}}} = \dfrac{{\text{d}}}{{\text{r}}} = \dfrac{{160}}{{80}} = 2$ hours.
After 8:10 AM, both the cars which are initially at different places A and B will meet each other in the next 2 hours.
Therefore, time when they will meet each = 8:10 AM + 2 hours = 10:10 AM
Hence, option A is correct.

Note: In this particular problem, since the given two cars are moving in opposite directions (or moving towards each other) that’s why the individual speed of the cars are added in order to determine the relative speed between them but if they were moving in the same direction then the relative speed between these cars would have been obtained by subtracting the individual speed of these cars.