Answer:
a. f < M < T
Explanation:
Let us take the right direction as positive.
Since Ted exerts a force T to the right his force is +T, Mario exerts a force M to the left, his force is -M. It is also given that Mario's force is half of Ted's force, so M = T/2. Finally, the frictional force , f is to the left, so it is -f. Let the net force be F and it is to the right since the box moves to the right.
So, +T - M - f = +F
Substituting M = T/2, we have
+ T -T/2 - f = F
+ T/2 - f = F
+T/2 = F + f
So, T = 2(F + f) and
M = T/2 = F + f
Since T = 2(F +f) = 2M, It follows that T > M
Also, since M = F + f, it follows that M > f
So, T > M > f ⇒ f < M < T
So, the answer is a.
