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Math Help - Word Problem-Calculus

  1. #1
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    Word Problem-Calculus

    It takes one corn mill 6 minutes to grind a 50 pound bag of corn into cornmeal, while it takes a slower mill 9 minutes to grind the same bag of corn. If both mills are working at the same time, how long would it take to grind 1500 pounds of corn?



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  2. #2
    MHF Contributor Unknown008's Avatar
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    If they work together, they should take less time to make a 50 pound bag.

    This time is given by:

    \frac{1}{t_1} + \frac{1}{t_2} = \frac{1}{t_{total}}

    Using the given values, we get:

    \frac{1}{6} + \frac{1}{9} = \frac{5}{18}

    So, the total time is 18/5 = 3.6 hours.

    It takes 3.6 hours to make a 50 pound bag.

    You can now use proportions to find the time it takes for 1500 pound of corn to be gound.
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  3. #3
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    Thanks

    Thank you, but if it takes 6 minutes for one person to do 50 pounds then how would it take 3.6 hours to to it together?
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  4. #4
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    Rate Mill 1: R_1 = 50/6
    Rate Mill 2: R_2 = 50/9

    Combined Rate R_t = R_1 + R_2

    Thus: Time = 1500 / (50/6 + 50/9) = 30/(1/6 + 1/9) = 108 min
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  5. #5
    MHF Contributor Unknown008's Avatar
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    Quote Originally Posted by skweres1 View Post
    Thank you, but if it takes 6 minutes for one person to do 50 pounds then how would it take 3.6 hours to to it together?
    Right, actually, I it was 3.6 minutes, and not 3.6 hours.

    Then, taking from there, you can use proportions to solve the rest.

    50 pounds are ground in 3.6 minutes.
    1 pound is ground in 3.6/50 minutes.
    1500 pounds are ground in 3.6/50 * 1500 = 108 minutes.
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  6. #6
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    Quote Originally Posted by skweres1 View Post
    It takes one corn mill 6 minutes to grind a 50 pound bag of corn into cornmeal, while it takes a slower mill 9 minutes to grind the same bag of corn. If both mills are working at the same time, how long would it take to grind 1500 pounds of corn?



    Please Help, Thanks!!!!
    When two or more things work together, their speeds ad. The speed of the fist corn mill is 50 pounds per 6 minutes or 50/6= 25/3 pounds per minute. The speed of the second is 50/9 pounds per minute. Together they can grind 50/9+ 25/3= 50/9+ 75/9= 125/9 pounds per minute. The will grind 1500 pounds in (1500)(125/9) minutes.
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