SOLUTION: a boat travels 1 km upstream and 1 km back. The time for the round trip is 5 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 803333: a boat travels 1 km upstream and 1 km back. The time for the round trip is 5 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 kph
current speed 4 kph

against current x- 4 kph
with current x+ 4 kph

Distance= 1 miles

Time against + time with = 5 hours
t=d/r

1 /( x + 4 ) + 1 /(x - 4 ) = 5

LCD = (x - 4 ) ( x + 4 )
1 *( x - 4 ) + 1 (x + 4 ) = 5 (x^2 - 16 )
1 x - -4 + 1 x + 4 = 5 ( x ^2 - 16 )
2 x = 5 x ^2 -80
5 x ^2 - -2 x - 80

Find the roots of the equation by quadratic formula

a= 5 , b= -2 , c= -80

b^2-4ac= 4 + 1600
b^2-4ac= 1604
%09sqrt%28%091604%09%29=%0940.05%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=( 2 + 40.05 )/ 10
x1= 4.20
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 2 -40.05 ) / 10
x2= -3.80
Ignore negative value
boat speed 4.205 kph

m.ananth@hotmail.ca