RIP
A train enters into a tunnel AB at A and exits at B. A jackal is sitting at O in another bypassing tunnel AOB. A cat is sitting at P inside the tunnel AB making the shortest possible distance between O and P, such that AO=30km and PB=32km.When a train before entering into the tunnel AB blows the whistle somewhere before A, the jackal and cat run towards A, they meet with an accident (with the train) at the entrance A. The ratio of speeds of the jackal and the cat is:
Details and Assumptions- The jackal and the cat both take the same time to reach the entrance.
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1 solution
For min. possible distance between P and O, OP should be perpendicular to AB. Let AP be x OA^2=x^2 + OP^2 = 30 =>OB^2=OP^2 + 32^2 =>(x+32)^2=30^2+ OB^2 =>(x+32)^2= 30^2 +OP^2 + 32^2 =>(x+32)^2=30^2 + 30^2 - x^2 +32^2 =>x^2 + 32x-900=0 =>x=(-32+68)/2=18km
Let the speed of cat be Vc and speed of jackal be Vj. Thus, At the time of entrance, AP=Vc t=18 OA=Vj t=30 Vj/Vc=OA/AP=30/18=5/3