SOLUTION: A boat travels 3km upstream and 3km back. the time for the round trip is 10 hours. the speed of the stream is 5km/hr whats the speed of the boat in still water?

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Question 539707: A boat travels 3km upstream and 3km back. the time for the round trip is 10 hours. the speed of the stream is 5km/hr whats 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 5

against current x- 5 kph
with current x+ 5 kph

Distance= 3 km

Time against + time with = 10 hours
t=d/r
3 /( x + 5 ) + 3 /(x - 5 ) = 10

LCD = (x - 5 ) ( x + 5 )
3 *( x - 5 ) + 3 (x + 5 ) = 10
3 x - 15 + 3 x + 15 = 10 ( x ^2 - 25 )
6 x = 10 x ^2 - 250
10 x ^2 - -6 x - 250

Find the roots of the equation by quadratic formula

a= 10 , b= -6 , c= -250

b^2-4ac= 36 + 10000
b^2-4ac= 10036 %09sqrt%28%0910036%09%29=%09100.18%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=( 6 + 100.18 )/ 20
x1= 5.31
x2=( 6 -100.18 ) / 20
x2= -4.71
Ignore negative value
Boat speed = 5.31 mph
ma.ananth@hotmail.ca