Question

Rihanna works in a coffee shop approximately nines 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 Rihanna‘s 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 ?

Answer 1

`\text{Given that Rihanna works in a coffee shop approximately nine miles from}\\ \text{her apartment. And on her way to work, she always stops halfway}\\ \text{through to meet her best friend at the part.}\\ \\ \text{The distance of the part from her apartment is }=5x+2 \text{ miles}\\ \\ \text{and the distance from the park to the coffee shop is }(25x-8)\text{ miles}\\`

`\text{since the park is halfway, so the distnace from apartment to park}\\ \text{and park to coffee shop must be equal. so we have}\\`

`25x-8=5x+2\\ \\ \Rightarrow 25x-5x=2+8\\ \\ \Rightarrow 20x=10\\ \\ \Rightarrow x=(10)/(20)\\ \\ \Rightarrow x=(1)/(2)`

Hence the value of x is 1/2