Question 1029727
rt = d
d = 24
rt = 24


(r+6)(t-9) = 24
simplify to get rt - 9r + 6t - 54 = 24


rt = 24
solve for r to get r = 24/t


replace r with 24/t in the equation of rt - 9r + 6t - 54 = 24 to get:
24t/t - 216/t + 6t - 54 = 24


multiply both sides of this equation by t to get:
24t - 216 + 6t^2 - 54t = 24t


subtract 24t from both sides of this equation and combine like terms and reorder the terms in descending order of degree to get:
6t^2 - 54t - 216 = 0


factor out the gcf  of 6 to get:
t^2 - 9t - 36 = 0


factor this quadratic equation to get:
(t-12)(t+3)


solve for t to get:
t = 12 or t = -3
t = -3 can't be good because time is not negative, so you get t = 12.


when t = 12, rt = 24 becomes r*12 = 24 and solve for r to get r = 2.


you have r = 2
t = 12


rt = d becomes 2*12 = 24, confirming this is good.


r+6 = 8
t-9 = 3


(r+6)(t-9) = d becomes 8*3 = 24, confirming this is also good.


your solution is that he was riding at 2 miles per hour.