What route should Bill take (max min prob?) to get to finish point as quickly as possible?

The starting point of a race is on an island 4 miles offshore in a straight river. The finish point is on the riverbank, 6 miles downstream. Bill can swim at a rate of 6 mph and cycle at a rate of 12 mph. Assuming Bill can have his bicycle waiting anywhere on the bank (neglect influence of current in the river), what route should h take to get from the starting point to the finishing point as quickly as possible?

What route should Bill take (max min prob?) to get to finish point as quickly as possible?small business loans

let x be the miles downstream from starting point

total distance travel=m=12sqrt(4^2+x^2)+6(6-x) with interval(0,6)

m=12sqrt(16+x^2)+36-6x

dm/dt=12x/sqrt(16+x^2)-6=0

144x^2=36(x^2+16)

x=5.3miles

m(5.3)=84hr

m(0)=84hr

m(6)=86hr

therefore the distance from downstream can be 0, or 5 1/3 miles away and give minimum time

What route should Bill take (max min prob?) to get to finish point as quickly as possible?

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Is the width of the river needed to solve this problem?