An Olympic athlete is standing at the edge of one side of a 4.2km wide river and

Question

An Olympic athlete is standing at the edge of one side of a 4.2km wide river and wants to reach the point 8.4km downstream just along the edge of the opposite side. For this entire 8.4km stretch, the river is completely straight. The velocity of the current is negligible. The athlete can swim at 8.4km/hr and run at 16.8km/hr. If she is to swim first and then run second if necessary, how far down the stream should she swim if she is to make it to her destination point in the shortest time? Round your answer to the nearest four decimal places.

Explanation / Answer

If she lands a distance x downstream, then she
swims (4.2^2+x^2)
runs 8.4-x

So, the time taken is

t(x) = (4.2^2+x^2)/8.4 + (8.4-x)/16.8
find x where dt/dx=0
where solving for x = 73/5 KM

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