SOLUTION: The current of a stream moves at a speed of 5km/hr. A boat travels 31 km upstream back in 11 hours. What is the speed of the boat in still water? Round your answer to two decimal

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Question 726623: The current of a stream moves at a speed of 5km/hr. A boat travels 31 km upstream back in 11 hours. What is the speed of the boat in still water? Round your answer to two decimal places.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
I presume 31 km is up and down each way
boat speed x kph
current speed 5 kph

against current x- 5 kph
with current x+ 5 kph

Distance= 31 miles

Time against + time with = 11 hours
t=d/r

31 /( x + 5 ) + 31 /(x - 5 ) = 11

LCD = (x - 5 ) ( x + 5 )
31 *( x - 5 ) + 31 (x + 5 ) = 11 (x^2 - 25 )
31 x - -155 + 31 x + 155 = 11 ( x ^2 - 25 )
62 x = 11 x ^2 -275
11 x ^2 - -62 x - 275

Find the roots of the equation by quadratic formula

a= 11 , b= -62 , c= -275

b^2-4ac= 3844 + 12100
b^2-4ac= 15944
%09sqrt%28%0915944%09%29=%09126.27%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
x1=( 62 + 126.27 )/ 22
x1= 8.56
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 62 -126.27 ) / 22
x2= -2.92
Ignore negative value
boat speed 8.56 kph

m.ananth@hotmail.ca