(a)[3]
Every day, Anna travels $45\,\text{km}$ to get to work. On one day, the first $25\,\text{km}$ is covered at an average speed of $82\,\text{km h}^{-1}$. The rest of the distance takes $36$ minutes to complete. Calculate her average speed, in $\text{km h}^{-1}$, for the entire trip.
(b)[3]
Anna’s trip back home is $47\,\text{km}$, to the nearest kilometre. On one day, her journey home lasts $65$ minutes, to the nearest $5$ minutes. Calculate the upper bound of her average speed, in $\text{km h}^{-1}$, for the journey home.
(c)[2]
On any given day, the probability that Anna reaches work on time or early is $\dfrac{5}{8}$. Calculate the probability that she is late on both Monday and Tuesday. Give your answer as a fraction.