Two Cars Meeting Point

CAT 2019 Slot 1 · QA · Easy · Speed, Time and Distance

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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

12

Explanation

Let AP=dAP = d, so BP=3dBP = 3d. Let speed of Car 1 = 2v2v, speed of Car 2 = vv. Time taken by Car 1 to reach P: t1=d2vt_1 = \frac{d}{2v}. Time taken by Car 2 to reach P: t2=3dvt_2 = \frac{3d}{v}. Given t2−t1=1t_2 - t_1 = 1 hour = 60 minutes. 3dv−d2v=60⇒5d2v=60⇒d2v=12\frac{3d}{v} - \frac{d}{2v} = 60 \Rightarrow \frac{5d}{2v} = 60 \Rightarrow \frac{d}{2v} = 12 minutes. So Car 1 takes 12 minutes to reach P from A.

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