Algebra question using distance rate and time HELP?

Question

After making a trip of 126 miles, a person found that the trip would have taken one hour less time by increasing the speed by 8mph. What was the actual speed? So far I have this from the teacher.
126/r = 1+ (126/r+8)

Answer 1

The equation is not quite right. It should be 126/r = 1 + 126/(r+8).

The time it takes to make a trip at constant velocity is t = d/v. The first trip is made at v = r, so its time is 126/r. This would be reduced by 1 if r is increased to r+8. The time it takes at r+8 is 126/(r+8). This time is 1 less than the first or 126/r - 1 = 126/(r+8), which is the same as 126/r = 1 + 126/(r+8).

To solve, multiply both sides by the product r*(r+8) to get

126*(r+8) = r*(r+8) + 126*r

Then multiply out to get

126*r + 126*8 = r^2 + 8*r + 126*r

Finally:

r^2 + 8*r - 126*8 = 0

This is solved by the quadratic equation.