SOLUTION: A boat traveled downstream a distance of 45 miles and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours, find the average speed of the bo

Algebra ->  Human-and-algebraic-language -> SOLUTION: A boat traveled downstream a distance of 45 miles and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours, find the average speed of the bo      Log On


   

Question 468233: A boat traveled downstream a distance of 45 miles and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours, find the average speed of the boat relative to the water.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed x
current speed 20

against current x-20 mph
with current x+ 20 mph

Distance= 45 miles

Time against + time with = 3 hours
45/(x+20)+45/(x-20)=3
LCD = (x-20)(x+20)
45*(x-20)+45(x+20)= 3
45x-900+45x+900 =3(x ^2 -400)
90x=3x ^2-1200
3x^2-90 x-1200
Find the roots of the equation by quadratic formula
a= 3 , b= -90 , c= -1200
b^2-4ac=8100+ 14400
b^2-4ac=22500
sqrt%2822500%29=150%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=(90+150)/6
x1= 40
x2=( 90 -150 ) / 6
x2= -10
Ignore negative value
Speed of boat = 40 mph