A car moves at a constant speed from A place to B. By $8$ o'clock in the morning the car covered $1/6$ part of the planned route, and by $11$ o'clock in the morning of the same day $8/9$ part. What part of the planned route did the car cover by $10$ o'clock and $30$ minutes in the morning of the same day?
I tried using proportion to get the part of planned route, didn't get the right answer. Help appreciated
Between $8$AM and $11$AM, the car covered $\dfrac89 - \dfrac16 = \dfrac{13}{18}$ of the planned route. Since this is $3$ hours, the car covers $\dfrac{13/18}{3} = \dfrac{13}{54}$ of the planned route each hour.
From $8$AM to $10$:$30$AM is $2.5$ hours, so in that time the car covers $\dfrac{13}{54}\cdot\dfrac52 = \dfrac{65}{108}$ of the planned route. Add that to the $\dfrac16$ already covered by $8$AM, and we have that at $10$:$30$AM, the car has covered $\dfrac{65}{108} + \dfrac16 = \dfrac{83}{108}$ of the planned route.