©2018 Compass Learning TechnologiesLive Mathematics on the Web →The Beach Race

## The Beach Race

A beach race begins from a point, 4 km out to sea from one end of a 10km beach. Racers must swim to a point along the beach, and then run to the finish line.

If I can swim at 4 kph and run at 10 kph, to what point on the beach should I aim to land?

Can you find the landing point for which the time of the race will be as short as possible - as accurately as possible?

Drag point C to find the landing position which will result in the LONGEST time for the race.

There are two landing points which will result in a race time of exactly 2 hours. One of these is to swim directly to the point O and then run the full length of the beach (swimming the shortest possible distance).

Drag the point C to find the other landing point which will result in a 2 hour race.

Now build an algebraic model for the times for the race, letting the distance OC = x:

swimtime(x) =

runtime(x) =

racetime(x) =

Finally, plot the derivative of this RaceTime(x) function to locate the best place to land:

myderiv(x) =

myderiv(x) = 0 when x =

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