b$.$ A rocket moving in space, far from all other objects, has a speed of $10\mathrm{.}0$x$106$ m$/$s relative to the Earth. Its engines are turned on$,$ and fuel is ejected in a direction opposite the rocket$$s motion at a speed of $3\mathrm{.}0$x$105$ m$/$s relative to the rocket. What is the speed of the rocket relative to the earth once the rocket$$s mass is reduced to $1/6$ its mass?

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