find how many men are needed

Question

The number of hours h that it takes m men to assemble x machines varies directly as the number of machines and inversely as the number of men. If four men can assemble 12 machines in four hours, how many men are needed to assemble 36 machines in 8 hours?

Answer 1

h = kx/m, for some constant k

 

Since h = 4 when x = 12 and m = 4, 4 = k(12)/(4)

 

                                                               4 = 3k   So, k = 4/3

 

Therefore, h = (4/3)x/m

 

So, if h = 8 and x = 36, we have 8 = (4/3)(36)/m

 

                                                         8 = 48/m

 

                                                         8m = 48        m = 6