$4.$ The differential in a tractor has a ring gear with $60$ teeth driven by a bevel pinion with $20$ teeth. Both of the differential side gears are connected to the rear axle through a final drive planetary gear set with a $4\mathrm{.}94$:$1$ reduction. The differential input speed and torque is $550$ rpm and $2,050$ lbft $,$ respectively.

a$.$ Calculate the speed, torque and power of each rear axle assuming the vehicle is traveling straight ahead on a uniform level surface. $($Rear axle includes the final drive ratio.$)$

b$.$ Now assume the wheel driven by the left axle encounters poorer traction, resulting in a $\backslash (10\backslash \%\backslash )$ decrease in torque transmitting ability and also resulting in it to rotate $\backslash (30\backslash \%\backslash )$ faster than the wheel driven by the right axle. Again, calculate the speed, torque and power of each rear axle. Assume the input speed remains constant. $($Hint: You have two unknowns and will need two equations.$)$