Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

### Answer

Let the time taken for car 1 to reach P from A be x hours.

Speed of car 1 = AP/x

Given, BP = 3AP

Car 2 starts from B to A and reaches P one hour after car 1 reaches P.

So, speed of car 2 = 3AP/(x+1)

Also, the speed of car 2 is half that of car 1. So,

3AP/(x+1) = 1/2 × AP/x

6x = x + 1

x = 1/5

Time taken for car 1 to reach P from A is 12 minutes.