SOLUTION: A student did a word-processing job for $40. It took him 5 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated. How long did he expect that

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Question 737018: A student did a word-processing job for $40. It took him 5 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated. How long did he expect that it would take to do the job?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A student did a word-processing job for $40.
It took him 5 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated.
How long did he expect that it would take to do the job?
:
let x = expected hourly wage
then
(x-4) = actual hourly wage
:
predicted time = actual time - 5 hrs
40%2Fx = 40%2F%28%28x-4%29%29 - 5
multiply by x(x-4), results:
40(x-4) = 40x - 5x(x-4)
40x - 160 = 40x + -5x^2+20x
subtract 40x from both sides, arrange as a quadratic eq on the left
5x^2 - 20x - 160 = 0
simplify, divide by 5
x^2 - 4x - 32 = 0
Factors to:
(x-8)(x+4) = 0
the positive solution
x = $8 an hr expected
:
:
Find the expected hrs required:
40/8 = 5 hrs
Find the actual hrs:
40/4 = 10 hrs
------------------
difference: 5 hrs