Question

One student can paint a wall in 10 minutes. Another student can paint the same wall in 15 minutes. Working together, how long will it take for them to paint the wall?

5 minutes

6 minutes

8 minutes

12 minutes

Answer 1

one hour = 60 minutes

so if the first student can paint a wall in 10 minutes, they can paint 1/10 of a wall per minute
similar logic with the other student: 15 minutes, so they can paint 1/15 of a wall per minute

if we let t = # of minutes, then the first student paints (1/10)t walls in (t) minutes, and the second student paints (1/15)t walls in (t) minutes.

together, to complete one (1) whole wall, our equation is therefore:

(1/10)t + (1/15)t = 1, solve for t