**Question: **

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

**Show 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.

Speed of car $2=\frac{3 \mathrm{AP}}{\mathrm{x}+1}$

Therefore, $\frac{3 \mathrm{AP}}{\mathrm{x}+1}=\frac{1}{2}\left(\frac{\mathrm{AP}}{\mathrm{x}}\right)$

Or $\mathrm{x}=\frac{1}{5}$ . Time taken for car 1 to reach $\mathrm{P}$ from $\mathrm{A}$ is 12 min.

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