SOLUTION: This question is on inverse variation: Tell whether the table represents inverse variation. If so write the inverse variation equation and solve for y when x=40. Show work that su

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Question 734263: This question is on inverse variation:
Tell whether the table represents inverse variation. If so write the inverse variation equation and solve for y when x=40. Show work that supports your conclusions.
Travel time(x) speed(y)
36 50
50 36
60 30
75 24
I answered yes 36.50
but y=?(I don't know)what is the equation
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
y should be related to x according to y=k%2A%281%2Fx%29, if they are in inverse variation. k is some constant. That equation is equivalent to xy=k.

Check to see if this produces a reliable constant, k:

x_______y_______k=xy
30______50______1500
50______36______1800
60______30______1800
75______24______1800

The only data point that does not seem to have the same k value is the first one at x=30; all the rest have k=1800. The data seem to be reasonably inverse variation if x is great enough, or something beyond 30. How far below x=50 does k not be constant we do not know. We do not really have enough data to judge how good is the model at x=40. May k=1800 fits and maybe it does not fit.

If the model fits near or at x=40, then our model, y=1800%2A%281%2Fx%29 gives us:
y=1800%2A%281%2F40%29=45. This could only be an ESTIMATE, because, as explained, we do not know how good is our model for values of x below 50. For the best we have, maybe k is about 1650 at x=40 and maybe y=1650%2A%281%2F40%29=41.