Question 916085: I need help with this problem please
John is on an Island in Lake Cavenacci three miles from the nearest point on the shore. Hootersville is 5 miles away as the crow flies. John can row 2mph and walk 4mph. John wishes to travel to Hootersville by rowing and walking in the shortest time. How far from hootersville should John land his rowboat on the beach. Hint: Use graphics calculator
Can you please explain how to do it because I am unsure of how to set the problem up and have been unable to get the right answer.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! John is on an Island in Lake Cavenacci three miles from the nearest point on the shore.
Hootersville is 5 miles away as the crow flies.
John can row 2mph and walk 4mph.
John wishes to travel to Hootersville by rowing and walking in the shortest time.
How far from hootersville should John land his rowboat on the beach.
:
This can be represented as a right triangle, formed by the Island (I), the nearest point (N) on the shore, and the town (H)
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I.
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N.---------------.L-----x------.H
L represents the Landing point and x is distance from there to the town.
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Find the distance from the nearest point to the town, N-H
The hypotenuse is given "as the crow flies" I-H, as 5 mi
One leg = 3 mi
Using pythag
N-H = 
N-H = 
N-H = 4 mi
:
Now we deal with a new right triangle where the hypotenuse is I-L, the distance the boat will travel
One leg = 3 mi
The other leg (4-x)
I-L = 
I-L = 
I-L =  miles to the landing point
We know the walking distance from there to the town = x
Find the time; time = dist over speed, row speed = 2, walk speed = 4
t(x) =  + 
Enter this equation into your graphing calc
should look something like this
min time when x 2.27 mi from the landing point to the town
Y = 2.3 hrs for the trip
:
You can confirm this for yourself, find the time for each leg using the actual distance rowed and distance walked, by substituting 2.27 for x
Any questions, ankor@att.net
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