SOLUTION: Meg rowed her boat upstream a distance of 40 miles and then rowed back to the starting point. The total time of the trip was 14 hours. If the rate of the current was 3 mph, find th

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Question 903887: Meg rowed her boat upstream a distance of 40 miles and then rowed back to the starting point. The total time of the trip was 14 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 Time forward + time return = hours
current speed 3 mph

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

Distance= 40 miles

Time against + time with = 14 hours
t=d/r

40 /( x + 3 ) + 40 /(x - 3 ) = 14

LCD = (x - 3 ) ( x + 3 )
40 *( x - 3 ) + 40 (x + 3 ) = 14 (x^2 - 9 )
40 x - -120 + 40 x + 120 = 14 ( x ^2 - 9 )
80 x = 14 x ^2 -126
14 x ^2 - -80 x - 126 = 0

Find the roots of the equation by quadratic formula 5.12

a= 14 , b= -80 , c= -126

b^2-4ac= 6400 + 7056
b^2-4ac= 13456
%09sqrt%28%0913456%09%29=%09116%09 379.94
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=( 80 + 116 )/ 28
x1= 7.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 80 -116 ) / 28
x2= -1.29
Ignore negative value
boat speed 7 mph

m.ananth@hotmail.ca