SOLUTION: A 150 minute river cruise goes 14km upstream and then back again. The river has a current of 3km an hour going downstream. What is the boat's speed in still water and how long was

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A 150 minute river cruise goes 14km upstream and then back again. The river has a current of 3km an hour going downstream. What is the boat's speed in still water and how long was       Log On


   

Question 937920: A 150 minute river cruise goes 14km upstream and then back again. The river has a current of 3km an hour going downstream. What is the boat's speed in still water and how long was the upstream journey in minutes?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boat speed x km Time forward + time return = hours
current speed 3 km

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

Distance= 14 km

Time against + time with = 2.5 hours
t=d/r

14 /( x + 3 ) + 14

LCD = (x - 3 ) ( x +
14 *( x - 3 ) + 14
14 x - -42 + 14 x +
28 x = 2.5 x ^2 -22.5
2.5 x ^2 - -28 x - -22.5 =

Find the roots of the equation by quadratic formula

a= 2.5 , b= -28 , c= -22.5

b^2-4ac= 784 + 225
b^2-4ac= 1009
%09sqrt%28%091009%09%29=%0931.76%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=( 28 + 31.76 )/ 5
x1= 11.95
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 28 -31.76 ) / 5
x2= -0.75
Ignore negative value
boat speed 11.953 km/h
Time upstream = (14/8.953)*60 =94 minutes

m.ananth@hotmail.ca