SOLUTION: A boat travels 10 km upstream and 10 km 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 445844: A boat travels 10 km upstream and 10 km 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):
You can put this solution on YOUR website!
Boat speed x
current speed 4

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

Distance= 10 miles

Time agianst + time with = 10 hours
t=d/r
10/(x +4)+10/(x -4)=10
LCD =(x -4)(x+4)
10*(x-4)+10x+4)=10
10x-40+10x+40=10(x ^2-16)
20x=10x^2-160
10x ^2-20x-160 =0
Find the roots of the equation by quadratic formula

a= 10 b= -20 c= -160

b^2-4ac=400+6400
b^2-4ac=6800
sqrt(6800)=82.46
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=(20+82.46)/20
x1=5.12
x2=(20-82.46)/20
x2= -3.12
Ignore negative value
speed = 5.12 mph