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January 28, 2015

January 28, 2015

Posted by **Anonymous** on Tuesday, November 2, 2010 at 4:15pm.

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 3:30pm56

- calculus -
**H H Chau**, Friday, August 22, 2014 at 5:23pmdistance 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

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