SOLUTION: A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

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Question 734136: A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. 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):
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A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
let speed in still water = x km/h
with current x+4 km/h
against current speed = x-4 km/h
time up + time return = 10
7/(x+4)+7/(x-4)=10
multiply equation by (x+4)(x-4)
7(x-4)+7(x+4)= 10(x^2-16)
7x-28+7x+28 = 10x^2-160
14x=10x^2-160
10x^2-14x-160=0
/2
5x^2-7x-80=0

Find the roots of the equation by quadratic formula

a= 5 , b= -7 , c= -80

b^2-4ac= 49 + 1600
b^2-4ac= 1649
%09sqrt%28%091649%09%29=%0940.61%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=( 7 + 40.61 )/ 10
x1= 4.76
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 7 -40.61 ) / 10
x2= -3.36
Ignore negative value
boat speed 4.761 kph