SOLUTION: Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2 mph and can walk 5 mph. Wh

Question 937217: Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2 mph and can walk 5 mph. Where should she land her boat to reach the village in the least amount of time?
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat.
She can row 2 mph and can walk 5 mph.
Where should she land her boat to reach the village in the least amount of time?
:
Boat
|
|
2 mi
|
|
.----x-----*-------(6-x)--------V
* is the landing point which is (6-x) away from the village
:
The rowing distance to * equals the hypotenuse, which is
The walking distance from * to the village is (6-x)
f(x) = time to the village (time = dist/speed)
f(x) = +
Graph:
time = rowing time + walking time
y = +

minimum time occurs when x = .87 mi, 2.1 hrs is min time, therefore
land the boat: 6 - .87 = 5.13 mi from the village

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
t = +
------------
Find the derivative of t wrt x:
dt/dx =

x =~ 0.87287 miles
distance = 6 - x

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