SOLUTION: Meg rowed her boat upstream a distance of 5 miles and then rowed back to the starting point. The total time of the trip was 6 hours. If the rate of the current was 2 mph, find the

Algebra ->  Human-and-algebraic-language -> SOLUTION: Meg rowed her boat upstream a distance of 5 miles and then rowed back to the starting point. The total time of the trip was 6 hours. If the rate of the current was 2 mph, find the       Log On


   

Question 468234: Meg rowed her boat upstream a distance of 5 miles and then rowed back to the starting point. The total time of the trip was 6 hours. If the rate of the current was 2 mph, 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 2

against current x-2 mph
with current x+ 2 mph

Distance= 5 miles

Time against + time with = 6 hours
5 /( x + 2 ) + 5 /(x - 2 ) = 6

LCD = (x - 2 ) ( x + 2 )
5 *( x - 2 ) + 5 (x + 2 ) = 6
5 x - 10 + 5 x + 10 = 6 ( x ^2 - 4 )
10 x = 6 x ^2 - 24
6 x ^2 - -10 x - 24

Find the roots of the equation by quadratic formula
a= 6 , b= -10 , c= -24
b^2-4ac= 100 + 576
b^2-4ac=676
%09sqrt%28%09676%09%29=%0926%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=(10+26)/12
x1=3
x2=(10-26)/12
x2= -1.33
Ignore negative value
Speed of boat is 3 mph