Respuesta :
Answer:
It will take 9 hours with 4 painters to paint 720 feet of fence.
Step-by-step explanation:
Given that,
The time needed to paint a fence varies directly with the length of the fence
[tex]t\propto l[/tex] .......(1)
and inversely with the number of painters
[tex]t\propto \frac1P[/tex].....(2)
Combination of (1) and (2) is
[tex]t\propto \frac lP[/tex]
where t represents time, [tex]l[/tex] represents length of fence, P represents number of painters.
Again we can write the above equation as
[tex]\frac{t_1}{t_2}=\frac{\frac{l_1}{l_2}}{\frac{P_1}{P_2}}[/tex]
[tex]\frac{t_1}{t_2}=\frac{l_1P_2}{l_2P_1}[/tex]
Given that,
It takes 7 hours with 2 painters to paint 280 feet of fence .
We need to find time to paint 720 feet of fence with 4 painters.
[tex]t_1[/tex]=7 hours, [tex]l_1[/tex]=280 feet, [tex]P_1[/tex]=2,
[tex]t_2[/tex]=? , [tex]l_2[/tex] = 720 feet, [tex]P_2[/tex]=4
[tex]\therefore \frac{7}{t_2}=\frac{280\times 4}{720\times 2}[/tex]
[tex]\Rightarrow \frac{t_2}{7}=\frac{720\times 2}{280\times 4}[/tex]
[tex]\Rightarrow {t_2}}=\frac{720\times 2\times 7}{280\times 4}[/tex]
[tex]\Rightarrow t_2=9[/tex]
It will take 9 hours to paint 720 feet of fence with 4 painters.
