SOLUTION: Sue rowed her boat across and back lake bend in 3 hours. if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going. w

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Sue rowed her boat across and back lake bend in 3 hours. if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going. w      Log On


   

Question 290323: Sue rowed her boat across and back lake bend in 3 hours. if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going.
would it be 7 over x plus 7 over x-2=3?
I have to solve it using the quadratic formula. Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Sue rowed her boat across and back lake bend in 3 hours.
if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going.
:
Yes, it could be:
7%2Fx + 7%2F%28%28x-2%29%29 = 3
Multiply by x(x-2), results
7(x-2) + 7x = 3x(x-2)
:
7x - 14 + 7x = 3x^2 - 6x
:
14x - 14 = 3x^2 - 6x
combine like terms to have a quadratic equation
0 = 3x^2 - 6x - 14x + 14
:
3x^2 - 20x + 14 = 0
:
the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem a=3; b=-20; c=14
x+=+%28-%28-20%29+%2B-+sqrt%28-20%5E2-4%2A3%2A14+%29%29%2F%282%2A3%29+
:
x+=+%2820+%2B-+sqrt%28400-168+%29%29%2F6+
:
x+=+%2820+%2B-+sqrt%28232+%29%29%2F6+
Two solutions
x+=+%2820+%2B+15.23%29%2F6+
x = 35.23%2F6
x = 5.87
and
x+=+%2820+-+15.23%29%2F6+
x = 4.77%2F6
x = .795
:
The reasonable solution: x = 5.87 mph, her rate going
:
:
Check solution by finding the times coming and going
7/5.87 = 1.19, going
7/3.87 = 1.81, returning
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total = 3 hrs