working alone, angie can process the payroll in 5 hours while pam can finish in 6 hours. how long would it take pam and angie to do the job

T1 = 5 h

T2 = 6 h

T = T1*T2/(T1+T2) = 30/11 = 2.73 h.

To find out how long it would take Pam and Angie to process the payroll if they worked together, we can use the concept of work rates.

First, let's find out how much work each person can do in one hour. If Angie can process the payroll in 5 hours, then her work rate is 1/5 of the job per hour. Similarly, if Pam can finish in 6 hours, her work rate is 1/6 of the job per hour.

To calculate the combined work rate when they work together, we can add the individual work rates. So, Angie and Pam's combined work rate per hour would be 1/5 + 1/6.

To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 5 and 6 is 30. So, let's convert the fractions to have a denominator of 30:

1/5 = 6/30 (multiplied numerator and denominator by 6)
1/6 = 5/30 (multiplied numerator and denominator by 5)

Now, we can add the fractions:

6/30 + 5/30 = 11/30

Therefore, Angie and Pam can process 11/30 of the job per hour when working together.

To find out how long it would take them to finish the entire job together, we can divide the total job (1) by their combined work rate (11/30):

1 / (11/30) = 30/11

Therefore, it would take Pam and Angie approximately 2.73 hours (or 2 hours and 44 minutes) to complete the payroll if they worked together.