SOLUTION: a boat travel 10 kilometer. upstream and 10 kilometer. back. the trip upstream and back takes 1.5 hours. If the speed of the current is 5 kilometer. per hour what is the speed of t

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Question 497459: a boat travel 10 kilometer. upstream and 10 kilometer. back. the trip upstream and back takes 1.5 hours. If the speed of the current is 5 kilometer. per hour what is 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= 10 km

Time against + time with = 1.5 hours
10 /( x + 5 ) + 10 /(x - 5 ) = 1.5

LCD = (x - 5 ) ( x + 5 )
10 *( x - 5 ) + 10 (x + 5 ) = 1.5
10 x - 50 + 10 x + 50 = 1.5 ( x ^2 - 25 )
20 x = 1.5 x ^2 - 37.5
1.5 x ^2 - -20 x - 37.5

Find the roots of the equation by quadratic formula

a= 1.5 , b= -20 , c= -37.5

b^2-4ac= 400 + 225
b^2-4ac= 625 %09sqrt%28%09625%09%29=%0925%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=( 20 + 25 )/ 3
x1= 15
x2=( 20 -25 ) / 3
x2= -1.67
Ignore negative value
15 mph=speed of boat
m.ananth@hotmail.ca