The first time I saw a worker rate problem was within the movie “Little Big League.” I don’t really like how it was solved in the movie, but there are definitely some humorous moments in the clip:

*“If Joe can paint a house in 3 hours and Sam can paint the same house in 5 hours, how long does it take for them to do it together?”*

**The key to solving a worker rate problem is to convert the word problem into single hour (hourly) rates.**

“Joe can paint a house in **3 hours**,” in the form of an hourly rate, means “Joe can paint **1/3** of a house in **1 hour**.”

“Sam can paint the same house in **5 hours**” means “Same can paint **1/5** of the same house in **1 hour**.”

When we add **1/3** and **1/5**, we get the combined hourly rate of both Joe and Sam working together. Since their least common multiple is 15, we’ll add **5/15** to **3/15**.

**5/15** + **3/15** = **8/15** **of a house per hour (combined rate of Joe and Sam)**

Now we go back and reference the question to see exactly what they are asking for, as **8/15** is not the final answer. We want to know how many **hours **it will take to finish painting a **single** house. Using our combined rate, mathematically that would be:

**( 8/15 house per hour) x (number of hours) = 1 house**

To get to the “**number of hours**” variable, we simply divide “**1 house**” by the combined hourly rate: **8/15**.

This gives us a final answer of **15/8** or **1 and 7/8**.

Be weary of variations the GMAT may try to throw at you. For example, if the question were to state, “Joe can paint **3 houses** in **one hour**,” the fraction for an hourly rate would be **3/1**. If the question were to state Joe can paint **2 houses** in **3 hours**,” the fraction for an hourly rate would be **2/3**.

Also make sure to check carefully what the question is asking for at the end. A GMAT question like this could easily try to throw you off at the end by asking how many hours does it take to paint 3 houses.

This can be dealt with easily by simply changing the right hand side of the previous formula from 1 house to **3 houses**.

**( 8/15 house per hour) x (number of hours) = 3 houses**

That gives us a final answer of **45/8** or **5 and 5/8**.

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