SOLUTION: A boat travels 10km upstream and 10km back. The time for the roundtrip is 5 hours. The speed of the stream is 2km/hour. What is the speed of the boat in still water?

Question 333302: A boat travels 10km upstream and 10km back. The time for the roundtrip is 5 hours. The speed of the stream is 2km/hour. What is the speed of the boat in still water?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the speed of the boat in still water be x kmph
speed of current =2kmph
..
speed downstream = x+2
speed upstream = x-2
..
distance both ways = 10 km
time = distance / speed
..
time upstream + time downstream = 5 hours
10/(x+2)+10/(x-2) = 5
LCM = (x+2)(x-2)
10(x-2)+10(x+2) / (x-2)(x+2)= 5
10x-20+10x+20=5(x-2)(x+2)
20x=5x^2-20
5x^2-20x-20=0
divide by 5
x^2-4x-4=0
..
solve by quadratic equation formula
x= (-b+-sqrt(b^2-4ac))/2a
a=1,b=-4,c=-4
b^2-4ac = 16+16=32
x1=(4+sqrt32) /2
x1= 4.82 kmph
..
x2=(4-sqrt32) /2
x2= -0.82 ( Ignore)
the speed of boat in still water = 4.82 km/h

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