Problem Solving

Working alone at its constant rate, machine K took 3 hours to produce 1/4
of the units produced
last Friday. Then machine M started working and the two machines, working simultaneously at
their respective constant rates, took 6 hours to produce the rest of the units produced last Friday.
How many hours would it have taken machine M, working alone at its constant rate, to produce all
of the units produced last Friday?
A. 8
B. 12
C. 16
D. 24
E. 30

OA is d

To produce 1/4th Stock Machine K takes: 3 Hours
To produce 1 (complete) Stock Machine K takes: 3/(1/4) = 12 Hours

To produce 3/4th Stock Machine K+M take: 6 Hours
To produce 1 (complete) Stock Machine K+M take: 6/(3/4) = 8 Hours

Applying W = R X T

1/T = 1/Tk + 1/Tm

1/8 = 1/12 + 1/Tm

=> Tm = 24 hours (which is the time it takes the machine M to do the complete work by itself)

Hence (D)

thanks for the explaination!!