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Math Help - Regular Hourly Rate

  1. #1
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    Regular Hourly Rate

    John Ritter, who is paid time-and-a-half for hours greater than 40, had a gross weekly wage of $442 for 48 hours. What is his regular hourly rate?

    My work:

    I was not able to develope an equation that would lead me to the right answer.

    I know:

    John normally works 40 hours at x hours per hour.

    John worked an additional 8 hours for that week totalling 48 hours of work time.

    John makes time-and-a-half for hours over 40, which means he made time-and-a-half for 8 hours, right?

    My problem is gathering all this data to form an equation.

    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by blueridge View Post
    John Ritter, who is paid time-and-a-half for hours greater than 40, had a gross weekly wage of $442 for 48 hours. What is his regular hourly rate?

    My work:

    I was not able to develope an equation that would lead me to the right answer.

    I know:

    John normally works 40 hours at x hours per hour.

    John worked an additional 8 hours for that week totalling 48 hours of work time.

    John makes time-and-a-half for hours over 40, which means he made time-and-a-half for 8 hours, right?

    My problem is gathering all this data to form an equation.

    Thanks
    Call Mr. Ritter's rate of normal pay R. Then when he works overtime he gets paid R + 0.5R (time and a half.) So he worked 40 hours at R, totalling a pay of 40R. He also worked 8 hours at R + 0.5R, totalling a pay of 8(R + 0.5R). Thus his total pay is
    P = 40R + 8(R + 0.5R) = 442

    Can you solve this from here?

    -Dan
    Last edited by topsquark; June 11th 2007 at 05:43 PM. Reason: Slight typo
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  3. #3
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    ok

    Dan,

    You said:

    Call Mr. Ritter's rate of normal pay R. Then when he works overtime he gets paid R + 0.5R (time and a half.)

    Question:

    Can I also write 0.5R as R(1/2)?

    +++++++++++++++++++++++

    So he worked 40 hours at R, totalling a pay of 40R. He also worked 8 hours at R + 0.5R, totalling a pay of 8(R + 0.5)R. Thus his total pay is
    P = 40R + 8(R + 0.5)R = 442

    Question:

    Why did you take out R from the quantity (R + 0.5R)?...See above.

    Can you solve this from here?

    Let's see:

    40R + 8R + 4R = 442

    52R = 442

    R = $8.50, which is P = his regular hourly rate.

    Once the equation was set up, I was able to find the answer.

    However, setting up the proper equation from given word problem data is not easy to do.

    It never crossed my mind that (R + 0.5R) needed to be multiplied by the additional 8 hours John worked.

    I read this problem through and through and just could not find the answer.

    Only after you set up the equation was I able to find P = $8.50 per hour as John's regular hourly rate.

    How can I perfect the ability to create proper equations to solve certain word problems?

    If you did not know how to form the equation given above, what would you do to find the answer?

    Thanks
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by blueridge View Post
    Dan,

    You said:

    Call Mr. Ritter's rate of normal pay R. Then when he works overtime he gets paid R + 0.5R (time and a half.)

    Question:

    Can I also write 0.5R as R(1/2)?

    +++++++++++++++++++++++

    So he worked 40 hours at R, totalling a pay of 40R. He also worked 8 hours at R + 0.5R, totalling a pay of 8(R + 0.5)R. Thus his total pay is
    P = 40R + 8(R + 0.5)R = 442

    Question:

    Why did you take out R from the quantity (R + 0.5R)?...See above.

    Can you solve this from here?

    Let's see:

    40R + 8R + 4R = 442

    52R = 442

    R = $8.50, which is P = his regular hourly rate.
    You caught my posted answer before I noted the error. But you were able to fix the problem before you saw my correction so that is very good!

    Quote Originally Posted by blueridge View Post
    How can I perfect the ability to create proper equations to solve certain word problems?

    If you did not know how to form the equation given above, what would you do to find the answer?

    Thanks
    Pretty much the only answer I can give you is practice, practice, practice! Some people seem to be able to readily translate these questions into "Mathese" some aren't. So the best thing you can do is work with them until you gain some facility. Sorry that I can't give you a better strategy.

    -Dan
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