SOLUTION: 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 tak
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Question 95723: 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?
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Larry Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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?
:
Let A = 6 (Mary's individual time);
Let B = 8 (John's individual Time)
Then:
T = = = 3.42857 hrs
:
:
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 B = unknown staff member's time
Then = 4
:
Multiply both sides by (B+12)
12B = 4(B+12)
12B = 4B + 48
12B - 4B = 48
8B = 48
B = 48/8
B = 6 hrs the time of the unknown staff member
:
Check solution using the given function: = = 4 hrs
:
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