6 graffiti artists paint 4 walls in 2 hours. How long does it take 4 graffiti artists to paint 8 walls?

Question

6 graffiti artists paint 4 walls in 2 hours. How long does it take 4 graffiti artists to paint 8 walls?

$$\frac{6}{4} \times x=2$$ $$x=\frac{2}{\frac{6}{4} } =\frac{8}{6} =\frac{4}{3}$$

Is that the hourly rate for each individual grafitti painter?

How long does it take 4 graffiti artists to paint 8 walls?

$$\frac{4}{8} x=1,x=\frac{4}{3} \Rightarrow \frac{4}{8} \left( \frac{4}{3} \right) \times t=1\Rightarrow \frac{16}{24} t=1\Rightarrow 16t=24\Rightarrow t=\frac{24}{16} =\frac{3}{2}$$

Answer: $$\boxed{3/2 \text{h}}$$

Is this correct?

Answer 1

6 graffiti artists paint 4 walls in 2 hours. As an equation we could write this quite simply as $6g = 4w/2h$. Now we are asked to find the speed (walls per hour) of 4 graffiti artists, hence multiplying both sides by $4/6$ gives us the statement $4g = 16w/12h$. From this it is easy to find how long it takes for 8 walls to be painted by these 4 graffiti artists, for by simplifying the ratio we'll find $4g = 8w/6h$. 4 graffiti artists require 6 hours to paint 8 walls

Answer 2

$6$ graffiti artists painting $4$ walls in $2$ hours means one artist is responsible for $\frac{4}{6}$ walls in the $2$ hours. I assume same speed of all artists and equal split of work.

In $1$ hour, an artist does half of that, i.e., $\frac{\frac{4}{6}}{2}=\frac{2}{6}=\frac{1}{3}$ walls/h. Here I assume an artist performs equally over time.

From this, if you have $4$ artists, they paint $4\cdot\frac{1}{3}=\frac{4}{3}$ walls/h. With this "speed", $8$ walls are painted in $\frac{8}{\frac{4}{3}}=6$ h.