One of Maria and Josie's early tasks is printing and laminating signs to hang at local businesses around town. Working alone, Maria could print and laminate the signs in 4 hours. Josie, however, has better laminating equipment, so she could get the job done by herself in 2 hours. If each works for the same amount of time, how long will it take them working together to print and laminate the signs? Start by filling in the table with the missing values or expressions. Note that rate of work is a unit rate that describes the amount of the job completed in one hour.

Working together, it takes them 1 1/3 hours to complete the job.

Maria works at a rate of 1/4 of the job per hour, since she completes 1 job in 4 hours.

Josie works at a rate of 1/2 of the job per hour, since she completes 1 job in 2 hours.

Let x be the total number of hours it takes.

1/4x + 1/2x represents the time Maria and Josie work together. 1 will represent the entire job, since it is 100% of the job (100% = 100/100 = 1):

1/4x + 1/2x = 1

Find a common denominator; for this problem, we use 4:

1/4x + 2/4x = 1

Combine like terms:

3/4x = 1

Divide both sides by 3/4:

3/4x : 3/4 = 1 : 3/4

x = 1/1 : 3/4

x = 1/1 * 4/3

x = 4/3 = 1 1/3