Mathematics

azmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of 60 seconds.
The second time she went up the entire flight, she walked up some steps and ran up 28 steps. This took a total of 42 seconds. How long would Yazmin take if she walked up the entire flight of steps? (You may assume constant rates for walking and running.)

Professor REINY
I search every inch of question you solved tactically.........

Was wondering if you had come up with any easier way back then though or I'll painfully stick with this....

Wow wow wow

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  1. total number of steps ---- x
    rate of running up the stairs ----- r steps/sec
    rate of walking up the stairs ----- w steps/se

    Case1: runs 16 steps, walks x-16 steps
    16/r + (x-16)/w = 60
    16w + r(x-16) = 60rw **

    case2: runs 28 steps, walks x-28
    28/r + (x-28)/w = 42
    28w + r(x-28) = 42 rw ***

    divide ** by ***
    (16w + r(x-16)) / (28w + r(x-28) ) = = 60rw/(42rw) = 10/7
    10(28w) + 10r(x-28) = 112w + 7r(x-16)
    280w + 10rx - 280r = 112w + 7rx - 112r
    3rx = 168r - 168w
    rx = 56r - 56w

    time taken to walk all stairs = x/w, so we need to fudge the last equation
    rx = 56r - 56w
    divide by r
    x = 56 - 56w/r
    now divide by w
    x/w = 56/w - 56/r = 56( 1/w - 1/r)

    now I am stuck

    had 3 unknowns, but only 2 equations


    As to your last part of the post, I don't recall what question you are talking about
    Perhaps if you find the time and date it was posted ....

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    Reiny
  2. This particular question
    October 29 2015 this question was posted by DC

    You used a computer program to make a perfect guess

    Which I don't know how you were able to do it

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  3. Let
    x = number of steps
    r = time per running step
    w = time per walking step
    we have
    16r+(x-16)w = 60
    28r + (x-28)w = 42
    This gives us
    w = r + 3/2
    x = 168/(2r+3)
    Since x is an integer and x≥28, 2r+3 must be a factor of 168 ≤ 6
    Since r≥0, only 6 is possible.
    If 2r+3=6, then r = 3/2, and w = 3, and there are 28 steps
    walking the whole way would take 3*28 = 84 seconds

    There is another solution if 2r+3=4, r = 1/2
    Then w = 2, and there are 42 steps
    walking would again take 84 seconds

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    oobleck
  4. Didn't even know it showed up as the first entry in "Similar Questions"
    Looks like my basic approach is the same in both solutions, I recall making up
    such a program in the language of BASIC, and basically letting the computer
    try all the different possibilities

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    Reiny
  5. Thank you sir reiny....I read it and again and again and I like it

    And also sir obleck I understand it much better now thanks man

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