Question

A marathon runner has a pacer running with him in order to make sure that the runner maintains a certain pace (innumber of minutes per mile) during the race. Based on the runner's 1-mile split times, the equation for the line of best fit was y = 10.4x, where y is the number of minutes, and x is the distance covered in miles. It turns out that the pacer kept the runner at a pace that was about 7/8 of the intended pace. If the pacer had kept the runner at the intended pace, what would have been the equation of the line of best fit?

Answer 1

If the pace kept was about 7/8 of the intented pace, that means the intended pace is 1 over 7/8 of the pace kept.

So if the pace was 10.4, the intended pace would be:

$\frac{10.4}{\frac{7}{8}}=10.4\cdot\frac{8}{7}=11.886$

So the intended pace is 11.886, therefore the equation would be:

$y=11.886x$