SOLUTION: A Student did a word processing job for $24. It took him 1 hour longer than he expected, and therefore he earned $4 per hour less than he anaticipated. How long did he expect that

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Question 184576: A Student did a word processing job for $24. It took him 1 hour longer than he expected, and therefore he earned $4 per hour less than he anaticipated. 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 $24. It took him 1 hour 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 t = time he expected to do the job (in hrs)
then
24%2Ft = amt per hr anticipated
:
24%2F%28%28t%2B1%29%29 = actual amt per hr
;
anticipated amt/hr = actual amt/hr + $4
24%2Ft = 24%2F%28%28t%2B1%29%29 + 4
Multiply equation by t(t+1), results:
24(t+1) = 24t + 4t(t+1)
:
24t + 24 = 24t + 4t^2 + 4t
:
0 = 4t^2 + 24t - 24t + 4t - 24
:
4t^2 + 4t - 24 = 0; a quadratic equation
Simplify, divide by 4
t^2 + t - 6
Factor
(t+3)(t-2) = 0
positive solution
t = 2 hrs expected to do the job
:
:
Check solution by finding the per hr amt
24/2 = $12 per hr
24/3 = $8 per hr
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diff = $4 when he works one extra hr