SOLUTION: A camper paddles a canoe 2 miles downstream in a river that has a 2-mile-per-hour current. To return to camp, the canoeist travels upstream on a different branch of the river. It i

Question 548366: A camper paddles a canoe 2 miles downstream in a river that has a 2-mile-per-hour current. To return to camp, the canoeist travels upstream on a different branch of the river. It is 4 miles long and has a 1-mile-per-hour current. The total trip (both ways) takes 3 hours. Find the average speed of the canoe in still water.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
boat speed x mph
current speed downstream 2 mph
current speed upstream 1
Distance with current 2 miles
Distance against current 4 miles

speed with current x + 2 mph
speed against current x 1 mph
Total time = 3 hours
Time with current= 2 /( x + 2 )
time against current 4 / ( x -1 )

Time with current + time against = 3 hours

2 /( x + 2 ) + 4 /(x -1 ) = 3
LCD = ( x + 2 )* (x -1 )
multiply the equation by the LCD
we get
2*(x-1)+4(x+2)=3(x^2+1x-2)
2x-2+4x+8=3X^2+ 3x-6
6x+6=3x^2+3x+-6
3x^2-3x -12= 0
3x^2-3x-12 = 0
/ 3
1 X^2 -1 x -4 = 0

Find the roots of the equation by quadratic formula
a= 1 ,b= -1 ,c= -4

b^2-4ac= 1 + 16
b^2-4ac= 17
4.12

x1=( 1 + 4.12 )/ 2
x1= 2.56
x2=( 1 -4.12 ) / 2
x2= -1.56
Ignore negative value
boat speed = 2.56 mph
m.ananth@hotmail.ca

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