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 seven hours to paint 280 feet of fence with two painters, how long will it take four painters to paint 720 feet of fence?

Answer 1

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

$t\propto l$ .......(1)

and inversely with the number of painters

$t\propto \frac1P$.....(2)

Combination of (1) and (2) is

$t\propto \frac lP$

where t represents time, $l$ represents length of fence, P represents number of painters.

Again we can write the above equation as

$\frac{t_1}{t_2}=\frac{\frac{l_1}{l_2}}{\frac{P_1}{P_2}}$

$\frac{t_1}{t_2}=\frac{l_1P_2}{l_2P_1}$

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.

$t_1$=7  hours, $l_1$=280 feet, $P_1$=2,

$t_2$=? , $l_2$ = 720 feet, $P_2$=4

$\therefore \frac{7}{t_2}=\frac{280\times 4}{720\times 2}$

$\Rightarrow \frac{t_2}{7}=\frac{720\times 2}{280\times 4}$

$\Rightarrow {t_2}}=\frac{720\times 2\times 7}{280\times 4}$

$\Rightarrow t_2=9$

It will take 9 hours to paint 720 feet of  fence with 4 painters.