# How to Solve GMAT Worker Rate Problems

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.