SOLUTION: Abby rows 10km upstream and 10km back in a total time of 3hrs. The speed of the river is 5km/h. Find abby's speed in still water.

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Question 916873: Abby rows 10km upstream and 10km back in a total time of 3hrs. The speed of the river is 5km/h. Find abby's speed in still water.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boat speed x mph Time forward + time return = hours
current speed 5 mph

against current x- 5 km/h
with current x+ 5 km/h

Distance= 10 miles

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

10 /( x + 5 ) + 10 /(x - 5 ) = 3

LCD = (x - 5 ) ( x + 5 )
10 *( x - 5 ) + 10 (x + 5 ) = 3 (x^2 - 25 )
10 x - -50 + 10 x + 50 = 3 ( x ^2 - 25 )
20 x = 3 x ^2 -75
3 x ^2 - -20 x - -75 = 0

Find the roots of the equation by quadratic formula 5.12

a= 3 , b= -20 , c= -75

b^2-4ac= 400 + 900
b^2-4ac= 1300
%09sqrt%28%091300%09%29=%0936.06%09 379.94
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
x1=( 20 + 36.06 )/ 6
x1= 9.34
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 20 -36.06 ) / 6
x2= -2.68
Ignore negative value
boat speed 9.343 km/h

m.ananth@hotmail.ca