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Question 52823This 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 less an hour than he anticipated. How long did he expect that it would take to do the job?
This question is from textbook
Found 2 solutions by AnlytcPhil, ankor@dixie-net.com:
Answer by AnlytcPhil(1806)   (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 less an hour than he anticipated. How long did he
expect that it would take to do the job?
Let x = the number of hours he expected it to take him
Then x+1 = the number of hours it actually took him
Earnings per hour = (Earnings)/(number of hours)
Make this chart.
No of hours Earnings Earnings/hour
Anticipated job x $24 24/x
Actual job x+1 $24 24/(x+1)
The equation comes from:
>>...he earned $4 less an hour than he anticipated...<<
24/(x+1) = 24/x - 4
Can you solve that? If not post again.
It comes out to be a quadratic with solutions
x = 2 and x = -3. We discard the negative answer.
So he expected it to take him 2 hours.
Checking:
He did a word processing job for $24. He only expected it
to take him 2 hours, but it took him 3 hours instead. If
he had finished it in the 2 hours he expected it to take
him, then upon receiving $24 for the job, he would have
earned $12 per hour. However since it took him 3 hours,
then upon receiving $24, he only made $8 per hour, which
is $4 less per hour.
Edwin
Answer by ankor@dixie-net.com(22740)  (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 less an hour than he anticipated. How long did he expect that it would take to do the job?
:
Let t = time anticipated
:
Then hourly rate anticipated = 24/t
:
Actual time required = [t+1]
:
Then actual hourly rate = 24[t+1]
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Make an equation from the following statement
"Actual hourly rate + $4 = anticipated hourly rate"
:
[24/(t+1)] + 4 = [24/t]
:
To get rid of these annoying denominators, mult eq by t[t+1], then we have:
24t + 4[t(t+1)] = 24[t+1]
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Mult what's in brackets and you have:
24t + 4t^2 + 4t = 24t + 24
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Group like terms on the left:
4t^2 + 24t - 24t + 4t - 24 = 0
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Leaves us with our old friend, the quadratic equation:
4t^2 + 4t - 24 = 0
:
Simplify, divide by 4:
t^2 + t - 6 = 0
:
Easily factors to:
[t + 3][t - 2] = 0
:
t = +2 hr anticipated; [the positive solution is what we want here.]
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So we can say he anticipated 2 hrs with an hourly rate of 24/2 = $12/hr
However, he took 3 hrs, which is an hourly rate of 24/3 = $8/hr, $4 less
:
A lot of steps, but did it make sense to you?
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