<PRE><B>Question 937217</B>
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 {{{sqrt(x^2+2^2)}}}
The walking distance from * to the village is (6-x)
f(x) = time to the village (time = dist/speed)
f(x) = {{{sqrt(x^2+2^2)/2}}} + {{{((6-x))/5}}}
Graph:
time = rowing time + walking time
y = {{{sqrt(x^2+2^2)/2}}} + {{{((6-x))/5}}}
{{{ graph( 300, 200, -4, 5, -2, 3, (sqrt(x^2+4)/2)+((6-x)/5)) }}}
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  
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