SOLUTION: The current in a stream moves at 8mph. A boat travels 19 miles upstream and 19 miles downstream in a total time of 9 hours. What is the speed of the boat in still water? All I'v

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Question 432425: The current in a stream moves at 8mph. A boat travels 19 miles upstream and 19 miles downstream in a total time of 9 hours. What is the speed of the boat in still water?
All I've been able to come up with is that if it took 9 hours to go 38 miles the boat would be going an average of 4.222mph.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed x
current speed 8

against current x-8 mph
with current x+8 mph

Distance= 19 miles

Time against + time with wind = 9 hours
t=d/r
...
19/(x + 8)+19/(x-8)=9

LCD =(x-8)(x+8)
19*(x - 8)+19x+ 8)=9
19x-152+19x+152 =9(x ^2 -64)
38x=9x ^2-576
9x ^2-38x-576=0
Find the roots of the equation by quadratic formula
a= 9 b= -38 c= -576
b^2-4ac= 1444 + 20736
b^2-4ac= 22180 :sqrt(22180)=148.93
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(38+148.93)/18
x1=10.38 mph
x2=(38 -148.93 ) / 18
x2= -6.16 ( ignore negative)
speed = 10.38 mph