SOLUTION: A boat travels 8 km upstream and 8 km back. The time for the round trip is 2 hrs. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

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Question 600811: A boat travels 8 km upstream and 8 km back. The time for the round trip is 2 hrs. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed x mph
current speed 4 mph

against current x- 4 mph
with current x+ 4 mph

Distance= 8 miles

Time against + time with =2 hours
t=d/r

8/(x+4) +8/(x-4)= 2

LCD =(x-4)(x+4)
8*(x-4) +8(x+4) =2(x^2-16)
8x-32+8x+32=2(x ^2-16)
16 x = 2 x ^2 -32
2 x ^2 - -16 x - 32 =0
divide by 2
x^2-8x-16=0

Find the roots of the equation by quadratic formula

a= 1 , b= -8 , c= -16

b^2-4ac= 64 + 64
b^2-4ac= 128
%09sqrt%28%09128%09%29=%0911.31%09
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=( 8 + 11.31 )/ 2
x1= 9.66
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 8 -11.31 ) / 2
x2= -1.66
Ignore negative value
Boat speed 9.66 mph

m.ananth@hotmail.ca