math!

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You have 48 minutes to take an exam of 21 questions. After you finish the first 10 questions, you realize you must answer the remaining questions twice as fast to finish the exam.

How many questions per minute were you answering?

Also, how many questions per minute must you now answer to finish the exam on time?

  • math! -

    q = first questions/min
    2 q = final que/min

    t min for first ten
    48 - t min for final 11

    q t = 10 so t = 10/q

    q t + 2q(48-t) = 21
    10 + 96q - 20 = 21
    96 q = 31
    q = 31/96 questions/min
    so twice that = 62/96 to finish
    ========================
    check
    t = 960/31 = 30.97 min
    48-t = 17.03 min

    30.97 * 31/96 = 10
    17.03 * 62/96 = 11
    sum = 21 sure enough

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