Question

The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes 8 hours to paint 560 feet of fence with 3 painters, how long will it take 2 painters to paint 1,024 feet of fence? (*hint: combined variation)

Answer 1

`\begin{gathered} y=k((x)/(z)) \\ x=\text{ length of fence} \\ z=\text{ painters} \\ y=\text{ time} \\ \text{first point} \\ x=560 \\ z=\text{ 3} \\ y=8 \\ 8=k((560)/(3)) \\ k=8\cdot((3)/(560)) \\ k=0.043 \\ \sec ond\text{ point} \end{gathered}`