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A peacock is sitting on the top of the pillar, which is 9m high. from a point 27m away from the bottom of the pillar , a snake is coming to its hole at the

base of the pillar.Seeing the snake the peacock pounches on it. If their speeds are equal, at what distance from the hole is the snake caught.

Let x = the distance from the bottom of the pole to the snake when caught
then 27 - x = the distance from the snake's beginning to where it is caught

So using the thereom of Patagoras we have the distance from the top of
the pole to the snake we have sqr(x^2 + 9^2) and using d = rt for the
peacock gives us

sqr(x^2 + 81) = rt

For the snake

27-x = rt and then since their rates are the same then their times are the same and then rt is the same so
sqr(x^2 + 81) = 27 -x

square both sides giving us

x^2 + 81 = 27^2 - 54x + x^2

subtract x^2 from both sides and we have

81 = 729 - 54 x

then subtract 729 from both sides
-648 = -54x so s = 12 m