SOLUTION: A small motor boat travels 7mph in still water. It takes 6hrs. longer to travel 48 miles going up stream than it does going down stream. Find the rate of the current. (hint 7+x=rat

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Question 603637: A small motor boat travels 7mph in still water. It takes 6hrs. longer to travel 48 miles going up stream than it does going down stream. Find the rate of the current. (hint 7+x=rate going down stream and 7-x= rate going up stream. Round off your answer to the nearest tenth).
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed 7 miles
current speed = x

Speed with current 7 + x
Speed against current 7 - x

Distance = 48 miles

t=d/r

Time against current - Time with current = 6 hour

48 /( 7 - x)- 48 /( 7 +x) = 6
LCD= ( 7 - x)( 7 + x)
Multiply equation by LCD
We get
48(7+x)-48(7-x) =6*(7-x)(7+x)
336+48x-336+48 x= 6*(49-x^2)
96 x = 294 - -6 x^2
6 x^2 96 x + -294 = 0
Find the roots of the equation by quadratic formula
a= 6 ,b= 96 c -294
b^2-4ac= 9216 - 7056
b^2-4ac= 16272
sqrt%28%0916272%09%29= 127.56
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=( -96 + 127.56 )/ 12
x1= 2.63
x2=( -96 -127.56 ) / 12
x2= -18.63
Ignore negative value
speed = 2.6 mph
m.ananth@hotmail.ca