Question

Jason is on one side of a river 2 miles from the nearest point on the opposite shoreline. With a rowboat, he wants to reach a house 6 miles farther down the shore on the opposite shoreline. If Jason can row at a rate of 3mph and can walk at a rate of 5mph, find the least amount of time required to reach the house.

I am trying to find the best spot to land that will minimize time. I think I'm setting it up correctly, but then get stuck.

Answer 1

r t = d, t=d/r

Set the derivative of the following to zero and solve the result for x.\[\frac{\sqrt{x^2+4}}{3}+\frac{6-x}{5} \]\[\frac{5 x-3 \sqrt{x^2+4}}{15 \sqrt{x^2+4}}=0 \]\[x=\frac{3}{2} \]\[t=\frac{26}{15} \text{ hours }\]