Some students (aged 16 to 18), among those who had to tackle this exam problem, fled the room in tears. Their parents launched a petition demanding that the pass mark be lowered, since the exam was so superhumanly difficult. And to think that, for once, we had a funny and clever problem! Judge for yourself:
A crocodile is eyeing prey 20m further along on the other side of the river. It moves at different speeds on land and in water. The time taken by our caiman to reach the zebra can be minimized if it swims to a certain point P, x meters from the other side of the river, as shown in the diagram. This time, T, is given (in tenths of a second) by the formula:
a) (i) Calculate the time taken if the crocodile never walks on land.
(ii) Calculate the time taken if the crocodile swims as little as possible.
b) Between these two extremes, there is a value of x that minimizes the time taken by the crocodile. Find this value and calculate this minimum time. Was this wretched crocodile problem really worth so many tears?
