How do u solve this maximum horizontal force physics problem?

Question

This is one question.. A sled weighing 60.0 N is pulled horizontally across snow so that the coefficient of kinetic friction between the sled and the snow is .100. A penguin weighing 70.0 N rides on the sled. If the coefficient of static friction between the penguin and the sled is .700, find the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off.

Answer 1

The penguin must be accelerated at a rate exceeding Fp/Mp where Mp is the mass of the penguin and Fp the frictional force between the penguin and the sled. Fp = Mp*g*kp, where kp is the coefficient of friction between penguin and sled. The force pulling the sled minus the friction between sled and snow must accelerate the whole system at that rate. The acceleration of the sled + penguin is then (Fs-ks*Ms*g)/(Mp+Ms), where Fs is the force on the sled and Ms is the mass of the sled.

a(required for penguin to slide) = Mp*g*kp/Mp = kp*g
a(imparted to the sled by Fs) = (Fs-ks*Ms*g)/(Mp+Ms)

Equate these to get kp*g = (Fs-ks*Ms*g)/(Mp+Ms)

Solve for Fs

Answer 2

let mass of sled be M1 & mass of penguin be M2
equation of motion for sled
F(max)-f(s)-f(k)=M1a---A
equation of motion of penguin
f(s)=M2a------B
static friction= f(s)=49N; kinetic friction= f(k)=6N
a-- acceleration of sled & penguin;solving A&B
F(max)=104N