SOLUTION: Jose rode his boat 4 kilometers up a stream and then returned the same distance. The current in the stream was flowing at a speed of 3 km/h. If the round trip took JOse 1 hour and

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Question 875422: Jose rode his boat 4 kilometers up a stream and then returned the same distance. The current in the stream was flowing at a speed of 3 km/h. If the round trip took JOse 1 hour and 20 minutes, find speed of his boat in still water.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boat speed x km/h Time forward + time return = hours
current speed 3 km/h

against current x- 3 km/h
with current x+ 3 km/h

Distance= 4 miles

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

4 /( x + 3 ) + 4 /(x - 3 ) = 5/3

LCD = (x - 3 ) ( x + 3 )
4 *( x - 3 ) + 4 (x + 3 ) = 5/3 (x^2 - 9 )
4 x - -12 + 4 x + 12 = 5/3 ( x ^2 - 9 )
8 x = 5/3 x ^2 -15
5/3 x ^2 -8 x - 15 = 0
5x^2-24x-45=0
Find the roots of the equation by quadratic formula

a= 5 , b= -24 , c= -45

b^2-4ac= 576 + 900
b^2-4ac= 1476
%09sqrt%28%091476%09%29=%0938.42%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=( 24 + 38.42 )/ 10
x1= 6.24
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 24 -38.42 ) / 10
x2= -1.44
Ignore negative value
boat speed 6.242 km/h