PROCESSING CLAIMS. Joe takes x hours on the average to process a claim. whereas Ellen's average is 1 hour longer.
a) write a rational function C(x) that gives the number of claims that they process while working for an 8-hour shift.
b) Find C(c)
To write the rational function, let's analyze the information given:
Joe takes x hours on average to process a claim, whereas Ellen's average is 1 hour longer. This means Ellen takes (x + 1) hours on average to process a claim.
a) To find the number of claims processed by Joe and Ellen, we need to consider the time available in an 8-hour shift. Let's define C(x) as the number of claims processed:
For Joe, if he takes x hours to process one claim, then in 8 hours, he can process 8/x claims:
C(x) = 8/x
For Ellen, if she takes (x + 1) hours to process one claim, then in 8 hours, she can process 8/(x + 1) claims:
C(x) = 8/(x + 1)
Therefore, the rational function C(x) that gives the number of claims processed while working an 8-hour shift is:
C(x) = 8/x for Joe
C(x) = 8/(x + 1) for Ellen
b) To find C(c), we simply substitute the value c into the rational function C(x):
For Joe:
C(c) = 8/c
For Ellen:
C(c) = 8/(c + 1)
Replace c with the given value to obtain the number of claims processed by Joe and Ellen in an 8-hour shift.