Question 5684: I am stuck on this and keep thinking in circles. I would really appreciate your help. Here is the question that we are to use quadratic equations to solve.
She rows 12km upstream and 12 km downstream in 3hrs. The speed of her boat in still water is 9km/hr. find the speed of the stream.
This is what I have come up with so far. r= d/t
Upstream
d=12
r= x-9
t=
Downstream
d=12
r= x+9
t=
I'm not sure how to put all the information together to solve. I tried
12/(x-9) + 12/(x+9)= 3
Please help!
Found 2 solutions by prince_abubu, longjonsilver:
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! You are so in the right track. Your setup is almost all right. I'm thinking about the upstream rate, though. You put x - 9 for the upstream rate. I think it would be 9 - x. Say what!?
We agree that all speeds in a forward direction must be positive, right? If x - 9 was positive, that would force x (the rate of the stream) to be greater than 9, which, if you're moving upstream, won't let you move forward . (In fact, you'll actually be moving backwards). If she was able to move upstream, then obviously, the speed of the current had to have been less than the speed of her boat in still water. The way to have the current's speed less than the boat's speed in still water, and for the upstream net speed to be positive, the upstream rate would have to be 9 - x.
I hope that helped. You were so close. I'd say you did a good job, getting this far (setting up the problem) takes a lot.
Here's your equation:
 Solve for x and you'll get the current's speed.
Answer by longjonsilver(2297)  (Show Source):
You can put this solution on YOUR website! Your answer looks fine actually, well done. However, being a mathematician, I have my own tried and tested method, shown here.
As you say, speed = distance/time.
Let x=speed of the boat in still water.
Let t = time taken to travel upstream
Upstream:
speed = x-9
distance = 12
time = t
Downstream:
speed = x+9
distance = 12
time = 3-t
so, upstream, we get x-9 = 12/t and downstream, we get x+9 = 12/(3-t).
so, re-arrange for t, since we are not interested in that, and we wish to get rid of it:
t = 12/(x-9) and 3-t = 12/(x+9) --> t = 3 - 12/(x+9).
Equating these 2 gives us 12/(x-9) = 3 - 12/(x+9), which is 12/(x-9) + 12/(x+9) = 3 --> your equation :-).
So, multiply every term by (x+9)(x-9) -->
 . we can cancel some terms on the left hand side:
 --> divide everything by 3
--> 
So, factorise (not sure it does easily) or plug into the quadratic formula. I shall leave this for you to do. Good luck. Oh yes, check my working because i am not happy that the equation doesn't factorise...perhaps the answer is a nive fraction...work it out :-)
jon.
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