Rihanna works in a coffee shop approximately nine miles from her apartment she bikes every day from her apartment to the coffee shop and then back to her apartment in the evening. however, on her way to work, she always stops halfway through to meet her best friend at a park. if the distance from apartment to the park is (5x 2) miles and the trip from the park to the coffee shop is (25x -8) miles long, then what is the value of x?

Assume that Rihanna's apartment, the park, and the coffee shop lie on a straight line.

The distance from the apartment to the park is 5x² miles, and the distance from the park to the coffee shop is (25x - 8) miles.
Because the total distance is 9 miles, therefore
5x² + 25x - 8 = 9
5x² + 25x - 17 = 0

Solve with the quadratic formula.
x = (1/10) [-25 +/- (25²+340)] = 0.6064 or -5.6064
Reject the negative solution because we should not haave negative distance.

Therefore,
The distance from the apartment to the park = 5(0.6064²) = 1.839 miles
The distance from the park to the coffee shop = 25*06064 - 8 = 7.16 miles.

 x = 0.6064 miles