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 anticipated. How long did he expect that

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Question 188493This question is from textbook
: 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?
thanks This question is from textbook

Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
let x =hours expected to do job let A=earnings per hour
:
24/x=A.......eq 1
:
24/x+1=A-4..eq 2
:
substitute A's value from eq 1 into eq 2
:
24/(x+1)=(24/x)-4
:
24/(x+1)=(24-4x)/x
:
24x=(x+1)(24-4x).......cross multiplied
:

:
divided all terms by 4
:

:
x=2 and -3.....we cant have negative hours
:
so x=2 hours of expected work.......but it took 3 hours
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=400 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2, -3. Here's your graph:





Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=400 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2, -3. Here's your graph:
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