Machine A paints y units in 15 minutes and machine B paints 3y units in 30 minutes. In how many minutes will A and B, working together, paint 45y units?

Question: Machine A paints y units in 15 minutes and machine B paints 3y units in 30 minutes. In how many minutes will A and B, working together, paint 45y units?

Solution:
Machine A paints per minute = y/15 units
Machine B paints per minute = 3y/30 = y/10 units

∴ A and B together paint per minute = y/15 + y/10
= (2y + 3y)/30
= 5y/30
= y/6 units

So, to paint y/6 units, it takes 1 minute.

Hence, to paint 45y units, time needed = (45y × 6)/y = 270 minutes.