2022 THREE(e)

Megan cycles from her home, H, to school, S, each day.

She rides along a path from her home to point P at a constant speed of 10 kilometres per hour.
At point P, Megan cuts across a park, heading directly to school. When cycling across the park,
Megan can only cycle at 6 kilometres per hour.

At what distance from her home should she choose to cut across the park in order to make her
travelling time a minimum?

You must use calculus and show any derivatives that you need to find when solving this problem.