A kangaroo of mass 34 kilograms is standing near the right end of a cart of mass 52 kilograms (the cart and the kangaroo were originally at rest). The left end of the cart was originally 2.2 meters to the right of a duck (also at rest). The kangaroo was originally 11.8 meters to the right of the duck.  The duck did not move throughout this physics question, and no kangaroos or ducks were harmed.  The kangaroo jumped in the direction of the duck, and the kangaroo moved a distance 6.4 meters relative to the cart. The cart could roll toward or away from the duck with negligible friction.  The kangaroo landed on the cart and everything stopped moving. When the kangaroo landed on the cart, how far (in meters) was the kangaroo from the duck?

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