Question

The table below shows y, the average speed of a cyclist in miles per hour, and x, the time in hours that it takes the cyclist to complete a bicycle tour. Which rational function best models the data in the table?

Time, x
(hours)
Average Speed, y
(miles per hour)
12
8
16
6
9
18

Answer 1

Assuming the tour distance is fixed, speed and time are inversely proportional: y = D/x. From the first two pairs 12·8 = 96 and 16·6 = 96, so D = 96.

Thus the best rational model is y = 96/x. (Note: the third pair gives 9·18 = 162, so it is inconsistent with the same fixed-distance assumption.)