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Math Help - another fraction word problem

  1. #1
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    another fraction word problem

    I tried to figure out this question..and started it, but do not know how to continue....would anyone we able to give me a hand ??

    An airline passenger read for the first 1/9 of the flight, and watched the film for the next 8/15 of the flight. He managed to sleep for 3/4 of the remaining time. When he woke they were serving snacks, which filled another 20 minutes. After that there was only 1/45 of the total flight time left. How long did he sleep?

    Would anyone be able to draw a simple diagram...to explain this?

    I tired looking for the common denominator by adding all the fractions together..

    1/9+8/15+3/4+1/45=17/12
    then i dont know what to do ><
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  2. #2
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    Quote Originally Posted by lemontea View Post
    An airline passenger read for the first 1/9 of the flight, and watched the film for the next 8/15 of the flight. He managed to sleep for 3/4 of the remaining time. When he woke they were serving snacks, which filled another 20 minutes. After that there was only 1/45 of the total flight time left. How long did he sleep?
    One piece at a time.

    Rule #1 - Name stuff! s = Total Time of the Flight
    read for the first 1/9 of the flight
    s/9
    Travelled s/9 Still to go s - s/9 = 8s/9
    watched the film for the next 8/15 of the flight
    8s/15
    Travelled s/9 + 8s/15 = 29s/45 Still to go s - 29s/45 = 16s/45
    He managed to sleep for 3/4 of the remaining time
    Watch this one. It does NOT say 3/4 of the trip. It's 3/4 or the remaining trip.

    (3/4)*(16s/45) = 4s/15
    Travelled 29s/45 + 4s/15 = 41s/45 Still to go s - 41s/45 = 4s/45
    snacks, ...filled another 20 minutes
    This one's a little different, too. It's just 20 minutes.
    Travelled 41s/45 + 20 min Still to go 4s/45 - 20 min
    there was only 1/45 of the total flight time left.
    s/45 = 4s/45 - 20 min

    Can you solve for 's'? This will give the total time for the trip. This will not answer the question. What does the problem statement ask?

    The hardest part on this one is simply paying attention. One must read very carefully.
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  3. #3
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    The whole trip is 300 minutes or 5 hours.
    The question is asking for how long did the he sleep....hmm...im not sure wat to do next ><...subtract 300 minutes to all the activies he did on the flight??
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  4. #4
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    Quote Originally Posted by lemontea View Post
    I tried to figure out this question..and started it, but do not know how to continue....would anyone we able to give me a hand ??

    An airline passenger read for the first 1/9 of the flight, and watched the film for the next 8/15 of the flight. He managed to sleep for 3/4 of the remaining time. When he woke they were serving snacks, which filled another 20 minutes. After that there was only 1/45 of the total flight time left. How long did he sleep?

    Would anyone be able to draw a simple diagram...to explain this?

    I tired looking for the common denominator by adding all the fractions together..

    1/9+8/15+3/4+1/45=17/12
    then i dont know what to do ><
    Let x = total time of the flight, in minutes

    ----Read = (1/9) of x = (1/9)x = x/9 min.

    ----Film = (8/15) of x = (8x/15) min.

    ----Sleep = (3/4) of (x -x/9 -8x/15) = (3x/4 -3x/36 -24x/60) min.

    ----Snack = 20 min.

    ----Time left = (1/45) of x = x/45 min.

    So,
    x/9 +8x/15 +(3x/4 -3x/36 -24x/60) +20 +x/45 = x
    x/9 +8x/15 +3x/4 -3x/36 -24x/60 +20 +x/45 = x -------(i)

    What would be a common number to multiply to all that so that the fractions would be cleared? LCD or LCM will come to mind, which are good.
    But by inspection, 3*60 is a good one too.
    Clear the fractions, multiply both sides of (i) by 3*60,

    20x +96x +135x -15x -72x +3600 +4x = 180x
    Collect like terms,
    -12x = -3600
    x = -3600/(-12)
    x = 300 min.

    How long did he sleep?

    Sleep = 3x/4 -3x/36 -24x/60
    = 3(300)/4 -3(300)/36 -24(300)/60
    = 80 minutes -------------------------answer.
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  5. #5
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    I dont get this small part..how u got the numbers...

    you said :
    How long did he sleep?

    Sleep = 3x/4 -3x/36 -24x/60
    = 3(300)/4 -3(300)/36 -24(300)/60
    = 80 minutes -------------------------answer.

    where did 3x/36 and 24s/60 come from...and how come you have to minus that from 3/4??
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  6. #6
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    Quote Originally Posted by lemontea View Post
    I dont get this small part..how u got the numbers...

    you said :
    How long did he sleep?

    Sleep = 3x/4 -3x/36 -24x/60
    = 3(300)/4 -3(300)/36 -24(300)/60
    = 80 minutes -------------------------answer.

    where did 3x/36 and 24s/60 come from...and how come you have to minus that from 3/4??

    I think now that you are not reading all of I write/explain in my solutions.

    Let me copy-paste what I wrote in answering your question:

    Let x = total time of the flight, in minutes
    ----Read = (1/9) of x = (1/9)x = x/9 min.

    ----Film = (8/15) of x = (8x/15) min.

    ----Sleep = (3/4) of (x -x/9 -8x/15) = (3x/4 -3x/36 -24x/60) min.
    ----Snack = 20 min.

    ----Time left = (1/45) of x = x/45 min.


    See the "Sleep"?
    If you don't understand it yet, ask me again and I will explain it more.
    Oh, the (x -x/9 -8x/15) is what is left of the time, as mentioned here in your question, "He managed to sleep for 3/4 of the remaining time."
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