SOLUTION: Please help!! I have tried to come up with a solution...but I am majorly stuck and frustrated!! If I've made an error, I can't see it. And with what I do have, I have no idea what
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Question 212720This question is from textbook Introductory Algebra
: Please help!! I have tried to come up with a solution...but I am majorly stuck and frustrated!! If I've made an error, I can't see it. And with what I do have, I have no idea what the next step should be. ~ Thanks! Here's the problem and my attempt:
Boat Speed. The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
t(1) = 45/r-3 t(2) = 45/r+3 t(1) + t(2) = 8, where r is the rate of the boat in still water
45/(r-3)+ 45/(r+3)=8 The LCD is (r-3)(r+3)
((r-3) (r+3) (45/(r-3)) + ((r-3) (r+3) (45/(r+3)) = 8 (r-3)(r+3)
45 (r + 3) + 45 (r - 3) = 8 (r^2 – 9)
45r + 135 + 45r – 135 = 8r^2 – 72
90r = 8r^2 – 72
-90r -90r
0 = 8r2 – 90r – 72
Now What? I know the next step is to factor but I can’t determine a factorization in the form of (x + ?)(x - ?)…the best I can do is…
0 = 2 (r^2 – 45r – 32)
And IF this is the correct factoring answer…I have NO CLUE what to do next! PLEASE HELP!! This question is from textbook Introductory Algebra
You can put this solution on YOUR website! 8r^2 -90r-72 = 0
2(4r^2-45r-36) = 0
2(r-12)(4r+3) = 0
Positive solution:
r = 12
=============
Cheers,
Stan H.
You can put this solution on YOUR website! Boat Speed. The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
.
Applying the distance formula:
d = rt)
Solving for t:
t = d/r
.
Let r = speed of boat in still water
then
"time going upstream" + "time going downstream" = 8
.
45/(r-3) + 45/(r+3) = 8
Now, multiplying both sides by (r-3)(r+3):
45(r+3) + 45(r-3) = 8(r-3)(r+3)
Expanding:
45r+135 + 45r-135 = 8(r^2-9)
45r+45r = 8r^2-72
90r = 8r^2-72
0 = 8r^2-90r-72 (Exactly what you had)
Solving for r using the quadratic formula yields:
r = {12, -0.75}
We can toss out the negative answer leaving:
r = 12 mph
.
Details of quadratic to follow:
(