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March 30, 2017

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Anna and Julia each take a bicycle trip. Anna rides 20 miles in 1 1/3 hours. Julia rides 246 miles in 16 hours. Which has slower unit rate? By how much?

  • math - ,

    recall that speed or rate is distance traveled over time, or:
    speed, v = d/t

    thus, you compare Anna's speed and Julia's speed:
    Anna: v = 20/(1 1/3)
    Julia: v = 246/(16)
    *note: first convert mixed number to improper fraction before dividing.

    hope this helps. :)

  • math - ,

    so it would e 20/4 over 3? I don't get how I would divide that from 246/16

  • math - ,

    it's 20/(4/3),, first simplify this,,

  • math - ,

    how do you simifly that?

  • math - ,

    when dividing a number by a fraction, first get the reciprocal of the fraction,,
    *to get reciprocal: you just interchange the numerator and denominator, thus:
    reciprocal of 4/3 = 3/4
    now the operation becomes multiplication instead of division:
    20 * (3/4)

    i think you know how to do this. :)
    let me see your work.

  • math - ,

    which is 12? Then do I divide 12 and 246/16?

  • math - ,

    nope, it's not 12,,
    remember that a whole number can be written to:
    20 = 20/1
    now,
    20/1 * 3/4 = ?

    ..and we will not divide the answer by 246/16,, we will just compare them.

    first, let me see your answer.

  • math - ,

    Well 20 times 3 is 60
    1 times 4 is 4
    60/4

  • math - ,

    you're on the right track,,
    now, what is 60/4 ?

  • math - ,

    15/1

  • math - ,

    right~! :)
    now, we simplify 246/16,,
    since the numerator and denominator have a common factor 2, we can cancel it out:
    (2*123)/(2*8) = 123/8
    123/8 is in simplest form,, now change this to mixed number.

  • math - ,

    15 3/8

  • math - ,

    yes, that's right~! :)
    now comparing the speed:
    Anna: 15
    Julia: 15 3/8

    which of the two is slower (or has smaller speed)?
    then, "by how much" means you will get the difference:
    15 3/8 - 15 = ?

  • math - ,

    3/8

  • math - ,

    nope,, 15 3/8 is greater than 15,,
    it's like you have 15 whole pizza plus 3 slices, while the other has only 15 whole pizzas, that's why,
    15 3/8 > 15

    then, "by how much" means you will get the difference:
    15 3/8 - 15 = ?

  • math - ,

    oh, i see you already have an answer,,
    right. the difference is 3/8 m/s. :)

  • math - ,

    the answer is obvious, do math

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