Tom wants to catch a hare. He is standing 250 yards south from the hare. The hare starts moving due east. Tom, instead of moving in the northeast direction, moves in such a way that at every instant, he is going towards the hare. If speed of Tom is one and one-third times that of the hare, find the distance each traveled before he caught the hare.

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Jul 7th, 2006
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Deepak kumar Behera

Jul 12th, 2006

The hare starts from let point A. Let Tom stands at B which is 250m away
from A .Suppose they meet each other at point C. So joining A,B,C we get
perpendicular triangle.Now AB = 250yard, AC = s(assume distance covered by hare), BC= (3+1/3)s
Now applying the formulae
     s^2 + 250^2 = (3 + 1/3) ^2
    s= 600/{ (91)^(1/2) } i.e distance covered by hare
   Distance covered by Tom = (3+1/3)s

Debarghya

Sep 13th, 2006

Well the answer provided was not correct.
Lets have a look at the scenario:
according to the scenario the boy will take a CURVE not a straight line.
so using Pythagoras Theoram wont help.
In this case we get a curve with two tangents( X and Y axes) intersectin
at 90 degrees.If we draw two perpendicular lines from those tangents,they meet at a point which is the center of a circle and the path taken by the boy is the ARC.
Thus we get an ARC with 90 degrees at the center and radius is 250 feet or meters(because it forms a suare !)
Thus the lenght of the arc is: 2*pi*radius* (90/360)
                                         2* (22/ 7)*250 = 250*11/7= 392.85.
Thus the answer is 392.85.