Question 438718
Let the rates of Tessa and Gary be T and G.
Given that Tessa's rate is 9 miles per hour faster than Gary's rate.
So, Gary's rate is 9 miles per hour less than Tessa's rate.
Therefore G = T - 9 ...(1)
We know that rate = distance/time
Time taken by Tessa to cover 24 miles by bike is t1 = distance/ rate
                                          t1 = 24/T 
Time taken by Gary to cover 9 miles by walk is t2 = distance/rate
                                               t2 = 9/G
Given that tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles.
 So, t2 - t1 = 1
    9/G - 24/T = 1
(9T - 24G)/GT = 1
9T - 24G = GT

From equation (1), we have G = T - 9.
9T - 24(T-9) = (T-9)T
9T - 24T + 216 = T^2 - 9T
-15T + 216 = T^2 - 9T         [Add 15T to both sides of equation]
-15T + 216 + 15T = T^2 - 9T + 15T
216 = T^2 - 9T + 15T

216 = T^2 + 6T                [subtract 216 from both sides of equation]
216 - 216 = T^2 + 6T - 216
0 = T^2 + 6T - 216
T^2 + 6T - 216 = 0

*[invoke quadratic "T", 1, 6, -216]
Here T cannot be equal to -18.
Hence T = 12.
Therefore rate of Tessa's is 12 miles per hour.

Regards,
Sudheer(edurite.com)