SOLUTION: tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles. tessa's rate is 9 miles per hour faster than Gary's rate. find tessa's rate.

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Question 438718: tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles. tessa's rate is 9 miles per hour faster than Gary's rate. find tessa's rate.
Answer by sudheerb(5) (Show Source):
You can put this solution on YOUR website!
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

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -18. Here's your graph:

Here T cannot be equal to -18.
Hence T = 12.
Therefore rate of Tessa's is 12 miles per hour.
Regards,
Sudheer(edurite.com)