SOLUTION: robinson crusoe is shipwrecked on a desert island. his wrecked ship is 120 yards from the shore, 300 yards down the shore from the point on the shore closest to his ship. Crusoe ma

Question 1069897: robinson crusoe is shipwrecked on a desert island. his wrecked ship is 120 yards from the shore, 300 yards down the shore from the point on the shore closest to his ship. Crusoe makes many trips between the hut and the ship and wants to minimize the time each trip takes. He can walk 130 yards per minute and pole his raft 50 yards per minute. where on the shoreline should he moor his raft so that the trips can be made in minimum time? define the function that models the total time to make the trip as a function of x, the distance down the shoreline from the wreck. find the value of x that will minimize the total time Round to the nearest yard.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
robinson crusoe is shipwrecked on a desert island. his wrecked ship is 120 yards from the shore, 300 yards down the shore from the point on the shore closest to his ship.
Crusoe makes many trips between the hut and the ship and wants to minimize the time each trip takes. He can walk 130 yards per minute and pole his raft 50 yards per minute.
where on the shoreline should he moor his raft so that the trips can be made in minimum time?
define the function that models the total time to make the trip as a function of x, the distance down the shoreline from the wreck.
find the value of x that will minimize the total time Round to the nearest yard.
:
Wreck
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|
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120
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|
*----x-----\raft----(300-x)------Hut
Shore line
:
x = the distance from the point* opposite the wreck, to the raft
The distance from the point to the hut is given as 300 yds
Therefore, (300-x) = the distance from the raft to the hut
The distance across the water; the raft to the wreck is the hypotenuse of a right triangle
:
Total time = water time + walk time
T(x) =
Graphing this equation

minimum time occurs when x=50
The raft should be placed 300-50 = 250 yds from the hut
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