SOLUTION: A boat travels 2 km upstream and 2 km back. The time for the round trip is 10 hours. The speed of the stream is 3km/hr. What is the speed of the boat in still water?

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Question 805762: A boat travels 2 km upstream and 2 km back. The time for the round trip is 10 hours. The speed of the stream is 3km/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 kph
current speed 3 kph

against current x- 3 kph
with current x+ 3 kph

Distance= 2 miles

Time against + time with = 10 hours
t=d/r

2 /( x + 3 ) + 2 /(x - 3 ) = 10

LCD = (x - 3 ) ( x + 3 )
2 *( x - 3 ) + 2 (x + 3 ) = 10 (x^2 - 9 )
2 x - -6 + 2 x + 6 = 10 ( x ^2 - 9 )
4 x = 10 x ^2 -90
10 x ^2 - -4 x - 90 = 0

Find the roots of the equation by quadratic formula 5.12
iiiii
a= 10 , b= -4 , c= -90

b^2-4ac= 16 + 3600
b^2-4ac= 3616
%09sqrt%28%093616%09%29=%0960.13%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 0
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 4 + 60.13 )/ 20
x1= 3.21
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 4 -60.13 ) / 20
x2= -2.81
Ignore negative value
boat speed 3.207 kph