Understanding the problem

Imagine you have a job to do, like cleaning a big house.

• A man can clean the whole house in 10 days.
• A boy can clean the whole house in 15 days.
• A woman can clean the whole house in 30 days.

We want to know how long it will take for all three of them to clean the house together.

How fast can each person work?

To figure this out, we need to know how much of the house each person can clean in one day.

• The man can clean 1/10 of the house in one day.
• The boy can clean 1/15 of the house in one day.
• The woman can clean 1/30 of the house in one day.

Working together

If they all work together, they can clean more of the house each day.

• Together, they can clean 1/10 + 1/15 + 1/30 of the house in one day.
• If we do the math, we find out that together they can clean 1/5 of the house in one day.

How long will it take them to finish?

If they can clean 1/5 of the house in one day, it will take them 5 days to clean the whole house.

So, the man, woman, and boy together can clean the whole house in 5 days.

This is the same as saying they can finish the work together in 5 days.