Let's look at what we know.
We know she traveled 24 miles in all (12 running 12 biking), and we also know she spent 2.25 hours to finish the race. And we also know she rides 8 mph than she runs.
x= biking y=riding
x+y=2.25
12/x - 12/y = 8
Solve top equation for y and plug in
y=2.25-x
12/x - 12/(2.25-x) = 8
Get common denominators.
[12(2.25 - x)]/[x(2.25-x)] - [12(x)]/[x(2.25-x)]= [8(x)(2.25-x)]/[x(2.25-x)]
Let's simplify and only work with the top part.
27-24x=18-8x^2
Let's get everything to one side.
8x^2 -24x +9
x equals -x plus or minus the square root b squared minus 4 a c all over 2 a
24 plus or minus \sqrt{288} divided by 16
if you subtract you get a negative number so add 24 to the \sqrt{288} to get roughly 40. Then divide by 16 to get 2.56 mi/hr for running. Add 8 to get mph for biking.
Source of information: Michael J. from www.wyzant.com
