Posted by Anonymous on Tuesday, November 2, 2010 at 4:15pm.
A lighthouse is built on an exposed reef, 5.5 miles offshore. The shoreline is perfectly straight, and a town is located 6.5 miles downshore from the point on the shoreline nearest the lighthouse.
The lighthouse keeper needs to go from the lighthouse to the town to get fresh supplies. He can row a boat at 1.2 miles per hour, and run at 3.4 miles per hour. How far downshore towards the town should he land, if he wants to get to the town as quickly as possible?

calculus  Anonymous, Monday, May 13, 2013 at 3:30pm
56

calculus  H H Chau, Friday, August 22, 2014 at 5:23pm
distance of boat rowing = sqrt(5.5^2 + x^2)
distance of running = 6.5  x
total travel time
t = sqrt(5.5^2 + x^2)/1.2 + (6.5  x)/3.4
dt/dx = x/(1.2*sqrt(5.5^2 + x^2)  1/3.4
d^2t/dx^2 = +ve at any x
x is at its minimum when dt/dx=0
x/(1.2*sqrt(5.5^2 + x^2) = 1/3.4
x = 6/sqrt(253) * 5.5 = 2.075 miles
t = 4.899 + 1.302 = 6.201 hours