The distance remaining for a half marathon race over several minutes is shown in table. Use the information to determine the constant rate change in the minutes per mile.

Table:
Time (min) Distance Remaining (mi)
40 8
56 6
72 4
88 2

2 answers

If the rate is constant, then

t = md+b
Now plug in two pairs of values, say the first two.

8 = 40a + b
6 = 56a + b
So, a = -1/8 and b=13

t = -1/8 d + 13

Now check the other two pairs of values to make sure they agree.
time = (distance-13)/-.125

ex. (8 + -13)/-.125 = 40
(6 + -13)/-.125 = 56