SOLUTION: The speed of the current in the Yankaton River is 3 kilometers per hour. If a boat travels 18 kilometers downstream in this river and then returns to its starting point all in 4 1/

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Question 310467: The speed of the current in the Yankaton River is 3 kilometers per hour. If a boat travels 18 kilometers downstream in this river and then returns to its starting point all in 4 1/2 hours, what is the rate of the boat in still water?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the speed of the boat in still water be x km/hr.
Downstream
the speed will be x+3 km/hr.
Distance traveled is 18 km.
So time taken = 18/x+3
--
Upstream
the speed of the boat is x-3 mph.
Distance is 18km.
Time 18 / x-3
.
Add up the two .
18/x+3 + 18/x-3 = 9/2 hours
18(x-3)+18(x+3)= 9/2(x^2-9)
18x-54+1854 = 9x^2-81 / 2
2(36x)= 9x^2-81
72x=9x^2-81
9x^2-72x-81=0 ( divide by 9)
x^2-8x-9=0
x^2-9x+x-9=0
x(x-9)+1(x-9)=0
(x+1)(x-9)=0
x= -1 Or x=9
Speed cannot be negative
so boat speed in still water = 9 km/hr