Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 6a - Exponents and Rational Functions
Practice Problems
9. An application of a rational function is T = (AB)/(A+B),which gives the time, T, it takes for
two workers to complete a particular task where A & B represent the time it would take for
each individual worker to complete the identical task.
a) The monthly reports are due and the department manager has decided to try and
accelerate the completion of the report by assigning a team of two workers the task. Mary
has completed the monthly reports in an average of 6 hours over the past few months.
John, who had worked in Mary's capacity prior to a change in assignments, used to
complete the task in 8 hours. How quickly will Mary and John finish the report if they
work together? In this problem, Mary = A = 6 and John = B = 8.
b) The very next month, both Mary and John are out sick. The manager knows that Skip can
do the reports in 12 hours working alone, but the manager needs the work done in 4
hours. He needs to choose a staff member to work with Skip. How quickly would the
other staff member have to complete the report working alone if the two hope to
complete the report in 4 hours?
Let A = 12 (Skip's time)
Let T = 4
c) Sara takes 3 hours longer to paint a floor than it takes Katie. When they work together, it
takes them 2 hours. How long would each take to do the job alone?
Sara = A = (X+3) and Kate = B = X
Scottsdale Community College Page 259 Intermediate Algebra