SOLUTION: a river is flowing at a rate of 5kph a boat travels 12km upstream and 36 km downstream in a total of 9hrs.what is the speed of the boat in stilll water?

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Question 514279: a river is flowing at a rate of 5kph a boat travels 12km upstream and 36 km downstream in a total of 9hrs.what is the speed of the boat in stilll water?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed x mph
current speed 5 mph

Distance with current 36 miles
Distance against current 12 miles

spee with current x + 5 mph
spee against current= x -5 mph
Total time = 9 hours
Time with current= 36 /( x + 5 )
time against current 12 / ( x -5 )

Time with current + time against = 9 hours

36/(x + 5 ) + 12 /(x -5 ) = 9
LCD = ( x + 5 )* (x -5 )
multiply the equation by the LCD
we get
3*(x -5)+ 12 (x +5)= 9 (x^2 -25 )
36)x -180 + 12 x + 60 ) = 9 X^2 -225
48 x -120 = 9 X^2 -225
9 X^2 -48 x 120 + -225 = 0
9 X^2+ -48 x+ -105 = 0
/ 9
1 X^2 -5.33 x -11.67 = 0

Find the roots of the equation by quadratic formula

a= 1 ,b= -5.33 ,c= -11.67

b^2-4ac= 28.41 + 46.68
b^2-4ac= 75.09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 49.98
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%2812%29
x1=( 5.33 + 8.67 )/ 2
x1= 7 7
x2=( 5.33 -8.67 ) / 2
x2= -1.67
Ignore negative value
Boat speed = 7 mph