SOLUTION: A boat leaves port and sails in still water at 5.6 mph for 3.5 hours. The boat then turns at a 57º angle and sails at 4.9 mph for 4.25 hours. If the boat turns and heads directly f

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A boat leaves port and sails in still water at 5.6 mph for 3.5 hours. The boat then turns at a 57º angle and sails at 4.9 mph for 4.25 hours. If the boat turns and heads directly f      Log On

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Question 766435: A boat leaves port and sails in still water at 5.6 mph for 3.5 hours. The boat then turns at a 57º angle and sails at 4.9 mph for 4.25 hours. If the boat turns and heads directly for port at 6 mph, how long will it take it to reach port?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Port is point A.
The first turn of 57 degrees is done at point B.
The turn to return back to port occurs at point C.

Know that the angle at B is 180-57=123 degrees.
You can calculate AB and BC. Use Law of Cosines to find distance CA. The distance CA is the distance back to port.

AB is 5.6%283.5%29
BC is 4.9%284.25%29

MILES
19.6%5E2%2B20.825%5E2-2%2819.6%29%2820.825%29cos%28123%29=CA%5E2
817.84%2B816.34%2A%28-0.5446%29=CA%5E2
CA%5E2=373.229
highlight%28CA=19.3%29 MILES

How long in time to reach port from point C?
Rate given is 6 mph.
Rate*time=19.3
time=19.3%2F6
highlight%28time=3.27%29 approximately, hours