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Math Help - rate time problem

  1. #1
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    Unhappy rate time problem

    Tom can harvest the wheat in 20 minutes. Roza can harvest the wheat in 42 minutes. If they work together, how long does it take to harvest the wheat?

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  2. #2
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    re: rate time problem

    tom's rate of job performance ... (1 job)/(20 min)

    roza's rate of job performance ... (1 job)/(42 min)

    rate together in jobs/min ... (1/20) + (1/42)


    now use the relationship ...

    (rate together)(time in minutes together) = 1 job completed

    solve for (time in minutes together)
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  3. #3
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    Re: rate time problem

    [(1/20) + (1/42)]t = 1
    (2/420)t = 1
    (1/210)t = 1
    t = 210 minutes

    i think that i made somethig wrong
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  4. #4
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    Re: rate time problem

    Quote Originally Posted by joshuaa View Post
    [(1/20) + (1/42)]t = 1
    (2/420)t = 1
    (1/210)t = 1
    t = 210 minutes

    i think that i made somethig wrong
    forget how to add fractions?

    \frac{1}{20} + \frac{1}{42} = \frac{21}{420} + \frac{10}{420}

    try again
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    Re: rate time problem

    [(1/20) + (1/42)]t = 1
    [(21/420) + (10/420)]t = 1
    (31/420)t = 1
    t = 420/31 = 13.55 minutes (Rounded to 2 d.p)

    is the answer correct this time?
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  6. #6
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    Re: rate time problem

    Quote Originally Posted by joshuaa View Post
    [(1/20) + (1/42)]t = 1
    [(21/420) + (10/420)]t = 1
    (31/420)t = 1
    t = 420/31 = 13.55 minutes (Rounded to 2 d.p)

    is the answer correct this time?
    does the solution make sense? what do you think?
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  7. #7
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    Re: rate time problem

    it does not make sense. could you please explain more?
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  8. #8
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    Re: rate time problem

    Quote Originally Posted by joshuaa View Post
    it does not make sense. could you please explain more?
    why do you think it does not make sense?
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    Re: rate time problem

    the time should be more than 20 minutes.
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  10. #10
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    Re: rate time problem

    Quote Originally Posted by joshuaa View Post
    the time should be more than 20 minutes.
    come on Josh ... THINK!

    if it took you 20 minutes to do a job by yourself, would it take more or less time if you had help?
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  11. #11
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    Re: rate time problem

    lol it will take less if i got help from a faster lady, not 42 minutes
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  12. #12
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    Re: rate time problem

    C'mon Josh...by yourself, it takes you 20 minutes to do the job; Ok?
    So if you get ANY help whatsoever, including from slowest person around,
    it will then take less than 20 minutes to do the job...see that?

    Say it takes you 20 minutes to paint 20 doors.
    If you get help from a slow painter who can paint only 1 door in 19 minutes,
    then the job took 19 minutes, right? You only needed to paint 19...
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  13. #13
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    Re: rate time problem

    You're absolutely right, Wilmer. This means that there are some situations in which I will not get help at all. Imagine that the slower painter can paint 1 door in 20 minutes! Then what will happen? No help, right? But, what will happen to the last door?
    Last edited by joshuaa; March 17th 2012 at 11:54 AM.
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  14. #14
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    Re: rate time problem

    After you painted 19 doors, slowpoke will have painted 19/20 of the last door:
    so both of you will work together to finish the 1/20 of door left.
    In other words, if slowpoke is so slow he can only paint 1 square inch of a door
    after 19 minutes, then quits, you still save a little time because you don't have
    to paint that 1 square inch!

    Let's change your problem slightly:
    Art can do a job in 21 minutes. Ben can do the same job in 28 minutes.
    If they work together, how long does it take to do the job?

    Art, in 1 minute : 1/21 of job
    Ben, in 1 minute: 1/28 of job
    Art + Ben, in 1 minute : 1/21 + 1/28 = (28 + 21) / (21*28) = 49/588 = 1/12 of job
    So they take 12 minutes if working together.

    For a general case equation, let one worker's time = a and the other = b.
    So in 1 minute, 1/a + 1/b of job gets done.
    So working together = a*b / (a + b) minutes.
    Let's see: 21 * 28 / (21 + 28) = 588 / 49 = 12

    Similarly with your original problem:
    20 * 42 / (20 + 42) = 840 / 62 = ~13.548 minutes ; or ~13 minutes 33 seconds.

    Now go away and start painting doors !
    Last edited by Wilmer; March 17th 2012 at 03:16 PM.
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