- A competitor is running a 20 kilometre race.
She runs each of the first 4 kilometres at a steady pace of 6 minutes per kilometre. After the first 4 kilometres, she begins to slow down.
In order to estimate her finishing time, the time that she will take to complete each subsequent kilometre is modelled to be \(5 \%\) greater than the time that she took to complete the previous kilometre.
Using the model,
- show that her time to run the first 6 kilometres is estimated to be 36 minutes 55 seconds,
- show that her estimated time, in minutes, to run the \(r\) th kilometre, for \(5 \leqslant r \leqslant 20\), is
$$6 \times 1.05 ^ { r - 4 }$$
- estimate the total time, in minutes and seconds, that she will take to complete the race.