If y varies jointly as x and the cube of z and y=16 when x=4 and z=2 then y=0.5 when x=-8 and z=-3

k = 1/2

y = -108

Step-by-step explanation:

y varies jointly as x and the cube of z

y =kxz^3

We know y=16 when x=4 and z=2  so we can determine k

16 = k (4) 2^3

16 = k*4*8

16 = 32k

Divide each side by 32

16/32 = 32k/32

1/2 = k

y = 1/2 xz^3

Now y=? when x=-8 and z=-3

y = 1/2 * 8 (-3)^3

y = (1/2) *8 (-27)

y =4 (-27)

y = -108

they would have to work 32 hours.