in desperate need of help, PRECALC

a driver averaged 50 miles per hour on the round trip between akron, oh and Columbus, oh, 100 miles away. The average speeds for going and returning were x and y miles per hour, respectively.

a. show that y=25x/x-25


b. determine the vertical and horizontal asymptotes of the function.

c.using a graphing utility to graph the function

d. complete the table
x | 30 | 35 | 40 | 45 | 50 | 55 | 60|
y | | | | | | | |

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asked by Andy G
  1. time going = 100/x ---> from Time = distance/ rate
    time going = 100/y

    total time = 100/x + 100/y = (100y + 100x)/(xy)
    total distance = 200

    avg speed = total distance / total time
    = 200/( (100y+100x)/(xy) )
    = 200 (xy)/(100y+100x)
    = xy/(y+x)
    but avg speed = 50
    xy/(x+y) = 50
    xy = 50x + 50y
    xy - 50y = 50x
    y(x-50) = 50x
    y = 50x/(x-50) ----> not your answer
    ( one of us made a mistake)

    horizontal asymptote of my answer: y = 50
    vertical asymptote of my answer: x = 50

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    posted by Reiny
  2. went 200 miles total averaging 50mph so took 4 hours total

    going: time = 100/x
    returning time = 100/y
    so
    100/x + 100/y = 4

    25/x + 25/y = 1

    25 y + 25 x = xy

    xy - 25 y = 25 x

    y(x-25) = 25 x

    y = 25 x /(x-25)

    as x approaches 25, y becomes undefined, vertical asymptote

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    posted by Damon
  3. Damon, I am having a brain freeze.
    I know you answer is correct.
    Can you see the error in my solution?

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    posted by Reiny
  4. Found my error.

    from :
    = 200 (xy)/(100y+100x)
    = xy/(y+x)

    should be
    = 200 (xy)/(100y+100x)
    = 2xy/(y+x)

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    posted by Reiny
  5. Whew, sorry, did not see this until you found it.

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    posted by Damon

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