Math 133 Unit 3 Allegebra?

Question

Part 2: 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?

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?

Answer 1

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?

just substitute in values
A will represent the hours Mary takes
B will represent the hours John takes
A=6
B=8
T=(AB)/(A+B)=[(6)(8)]/(6+8)=48/14=24/7 hours


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?

now you are given T and A, and you are solving for B
T=4 hours
A=12 hours
B=?
T = (AB)/(A+B)
4=(12B)/(12+B)
cross multiply
4(12+B)=12B
48+4B=12B
48=8B
6=B
the other staff member must complete the work in 6 hours.

Answer 2

a) 6*8/(6+8) =48/14 = 3 3/7 hours

b) 12x/(12+x) =4
12x = 48+4x
8x = 48 --> x = 6 hours

Answer 3

You are just plugging numbers into that formula and solving for the one you don't know.

In part a you know A and B but not T. In part b you know A and T but not B. Just plug in what you know and solve.