Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

Joan and Jim run around the same circular track, starting together and running in the same direction....more below?

...Joan takes 3 minutes to complete one circuit of the track while Jim takes 74 minutes

to run the same distance. Joan passes Jim every x minutes. Find the value of x.

Update:

It's supposed to be 7 min sorry

2 Answers

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  • 3 weeks ago
    Favorite Answer

    Are you sure about the numbers? There seems to be quite a disparity between Joan's time and Jim's time.

    In any case, Joan runs 1/3 of the course every minute. Jim runs 1/74 of the course every minute.

    So every minute, Joan increases her distance ahead of Jim by 1/3 - 1/74 of a track length.

    1/3 - 1/74

    = 74/224 - 3/224

    = 71/224

    We want to know when Joan will lap Jim by getting exactly 1 lap ahead.

    (71/224)x = 1

    x = 1 / (71/224)

    x = 224/71

    x = 3 11/71 minutes

    In other words, she'll run a full lap and then about another 9.3 seconds and will catch up with Jim who has barely gone anywhere.

    If your numbers are different, just use this formula.

    Let A be Joan's time to complete one lap

    Let B be Jim's time to complete one lap

    x = AB / (B - A)

    For example, if Joan takes 3 minutes and Jim takes 7.5 minutes, we would have:

    x = (3 * 7.5) / (7.5 - 3)

    x = 22.5 / 4.5

    x = 45/9

    x = 5 minutes

    Answer:

    With your numbers, about 3 minutes 9.3 seconds

    Update:

    x = (3 * 7) / (7 - 3)

    x = 21/4

    x = 5 1/4 minutes

    Answer:

    With your revised numbers, 5 minutes 15 seconds

    • Puzzling
      Lv 7
      2 weeks agoReport

      As I said at the bottom, use the formula and plug in a=3, b=7.

  • Let d be the distance of the track

    Joan's speed (v) = d/t = d/3

    Jim's speed (v) = d/t = d/72

    Shouldn't be too hard to solve if you can imagine what's going on

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