SOLUTION: Meg rowed her boat upstream a distance of 91 mi and then rowed back to the starting point. The total time of the trip was 20 hours. If the rate of the current was 3 mph, find the a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Meg rowed her boat upstream a distance of 91 mi and then rowed back to the starting point. The total time of the trip was 20 hours. If the rate of the current was 3 mph, find the a      Log On


   

Question 766905: Meg rowed her boat upstream a distance of 91 mi and then rowed back to the starting point. The total time of the trip was 20 hours. If the rate of the current was 3 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 mph
current speed 3 mph

against current x- 3 mph
with current x+ 3 mph

Distance= 91 miles

Time against + time with = 20 hours
t=d/r

91 /( x + 3 ) + 91 /(x - 3 ) = 20

LCD = (x - 3 ) ( x + 3 )
91 *( x - 3 ) + 91 (x + 3 ) = 20 (x^2 - 9 )
91 x - -273 + 91 x + 273 = 20 ( x ^2 - 9 )
182 x = 20 x ^2 -180
20 x ^2 - -182 x - 180

Find the roots of the equation by quadratic formula
iiiii
a= 20 , b= -182 , c= -180

b^2-4ac= 33124 + 14400
b^2-4ac= 47524
%09sqrt%28%0947524%09%29=%09218%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=( 182 + 218 )/ 40
x1= 10.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 182 -218 ) / 40
x2= -0.90
Ignore negative value
boat speed 10 mph

m.ananth@hotmail.ca