SOLUTION: during a race a high performance sailboat traveled 54 miles with the wind in 3 hours. the return trip, against the wind, took 6 hours. find the rate of the boat in calm water and t

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Question 64640: during a race a high performance sailboat traveled 54 miles with the wind in 3 hours. the return trip, against the wind, took 6 hours. find the rate of the boat in calm water and the rate of the wind
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=boat's rate in calm water and
Let y=rate of wind
The boat's rate against the wind (x-y) was 54mi/6hr=9mi/hr.
The boat's rate with the wind (x+y) was 54mi/3hr=18mi/hr.
so we have:
(1) x-y=9mi/hr
(2) x+y=18mi/hr
adding the equations, we get:
2x=27mi/hr divide both sides by 2 we have:
x=13.5mi/hr rate of the boat in calm water
substitute in (1) and we get:
13.5mi/hr-y=9mi/hr
-y=9mi/hr-13.5mi/hr=-4.5mi/hr
y=4.5mi/hr rate of the wind
ck
13.5+4.5=18mi/hr
13.5-4.5=9mi/hr
Hope this helps. Happy holidays.-----ptaylor