Friday

October 24, 2014

October 24, 2014

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

**Answer this Question**

**Related Questions**

calculus - A lighthouse is built on an exposed reef, 5.5 miles off-shore. The ...

calculus - Given ensuing information, determine the least cost and the least ...

calculus - Given ensuing information, determine the least cost and the least ...

Math(module 4 Calculus) - (minimum commuting time) A lighthouse lies 2 miles ...

Calculus - A small resort is situated on an island that lies exactly 6 miles ...

calc - 15. Given ensuing information, determine the least cost and the least ...

Math - Need help with setting up an equation for this problem: A boat is sailing...

Calculus - A lighthouse is located on a small island 3 km away from the nearest ...

Calculus - A lighthouse is located on a small island 4 km away from the nearest ...

Calculus - Consider the illustration, which shows a rotating beam of light ...