Question

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?

Answer 1

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

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