One student can paint a wall in 16 minutes. another student can paint the same wall in 24 minutes. working together, about how long will it take for them to paint the wall?

Let's look at work rates per minute.

Together they can paint the wall in x minutes.
Working together, in 1 minute, they do 1/x of the job.

The student who paints the wall in 16 minutes does 1/16 of the job in 1 minute.
The student who paints the wall in 24 minutes does 1/24 of the job in 1 minute.
Together, they do 1/16 + 1/24 of the job in 1 minute, but from above, we see that together, they do 1/x of the job in 1 minute, so 1/16 + 1/24 must equal 1/x. That gives us our equation.

1/16 + 1/24 = 1/x

1/16 * 3/3 + 1/24 * 2/2 = 1/x

3/48 + 2/48 = 1/x

5/48 = 1/x

x = 48/5 = 9.6

It takes them 9.6 minutes, or about 10 minutes to do the job together.