SOLUTION: david canoes upstream a distance of 8 miles and then returns. The round-trip took 5 1/3 hours. The current of the stream was flowing at 2 miles per hour. What was david's canoeing

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Question 736351: david canoes upstream a distance of 8 miles and then returns. The round-trip took 5 1/3 hours. The current of the stream was flowing at 2 miles per hour. What was david's canoeing speed?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
canoe speed x mph
current speed 2 kph

against current x- 2 mph
with current x+ 2 mph

Distance= 8 miles

Time against + time with = 5 1/3 hours
t=d/r

8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3

LCD = (x - 2 ) ( x + 2 )
8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 )
8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 )
16 x = 5 1/3 x ^2 -21.33
5 1/3 x ^2 - -16 x - 21.33

Find the roots of the equation by quadratic formula

a= 5 1/3 , b= -16 , c= -21.33

b^2-4ac= 256 + 455.04
b^2-4ac= 711.04
%09sqrt%28%09711.04%09%29=%0926.67%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 0
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 1.33
x1=( 16 + 26.67 )/ 10.67
x1= 4.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 16 -26.67 ) / 10.67
x2= -1.00
Ignore negative value
canoe speed 4.000 mph

m.ananth@hotmail.ca

canoe speed x mph
current speed 2 kph

against current x- 2 mph
with current x+ 2 mph

Distance= 8 miles

Time against + time with = 5 1/3 hours
t=d/r

8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3

LCD = (x - 2 ) ( x + 2 )
8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 )
8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 )
16 x = 5 1/3 x ^2 -21.33
5 1/3 x ^2 - -16 x - 21.33

Find the roots of the equation by quadratic formula

a= 5 1/3 , b= -16 , c= -21.33

b^2-4ac= 256 + 455.04
b^2-4ac= 711.04
%09sqrt%28%09711.04%09%29=%0926.67%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 0
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 1.33
x1=( 16 + 26.67 )/ 10.67
x1= 4.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 16 -26.67 ) / 10.67
x2= -1.00
Ignore negative value
canoe speed 4.000 mph

m.ananth@hotmail.ca


canoe speed x mph
current speed 2 kph

against current x- 2 mph
with current x+ 2 mph

Distance= 8 miles

Time against + time with = 5 1/3 hours
t=d/r

8 /( x + 2 ) + 8 /(x - 2 ) = 5 1/3

LCD = (x - 2 ) ( x + 2 )
8 *( x - 2 ) + 8 (x + 2 ) = 5 1/3 (x^2 - 4 )
8 x - -16 + 8 x + 16 = 5 1/3 ( x ^2 - 4 )
16 x = 5 1/3 x ^2 -21.33
5 1/3 x ^2 - -16 x - 21.33

Find the roots of the equation by quadratic formula

a= 5 1/3 , b= -16 , c= -21.33

b^2-4ac= 256 + 455.04
b^2-4ac= 711.04
%09sqrt%28%09711.04%09%29=%0926.67%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 0
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 1.33
x1=( 16 + 26.67 )/ 10.67
x1= 4.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 16 -26.67 ) / 10.67
x2= -1.00
Ignore negative value
canoe speed 4 mph

m.ananth@hotmail.ca