Question

Two sisters like to compete on their bike rides. Stephanie can go 5 mph faster than her sister, Kathryn. If it takes Kathryn one hour longer than Stephanie to go 25.2 miles, how fast can Kathryn ride her bike?

Answer 1

9 mph

Explanation:

Let Kathryn can go x mph and Stephanie can go (x + 5) mph.

Therefore, Kathryn can go 25.2 miles in
`(25.2)/(x)` hours.

And Stephanie can go 25.2 miles in
`(25.2)/(x + 5)` hours.

Given that
`(25.2)/(x) - (25.2)/(x + 5) = 1`

⇒
`25.2[(5)/(x (x + 5)) ] = 1`

⇒ 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)