Answer:
9 mph
Step-by-step explanation:
Let Kathryn can go x mph and Stephanie can go (x + 5) mph.
Therefore, Kathryn can go 25.2 miles in [tex]\frac{25.2}{x}[/tex] hours.
And Stephanie can go 25.2 miles in [tex]\frac{25.2}{x + 5}[/tex] hours.
Given that [tex]\frac{25.2}{x} - \frac{25.2}{x + 5} = 1[/tex]
⇒ [tex]25.2[\frac{5}{x (x + 5)} ] = 1[/tex]
⇒ 126 = x² + 5x
⇒ x² + 5x - 126 = 0
⇒ (x + 14)(x - 9) = 0
⇒ x = -14 or x = 9
But x can not be negative, so x = 9 mph
Therefore, Kathryn can ride her bike at 9 mph. (Answer)
