I don't beleive you have enough information to correctly answer the question. What is the drag on the boat? What is the gravity factor in the equation? What is the rise rate of the stream?The water weights about 8lbs per gallon and is pushing agains the boat at 3 miles per hour. That is a lot of force to over come for a person paddling against it. Do not think it equates to two powered items moving toward each other.
surely if the booble is moving at 3 miles an hour towars you and your moving at 7 miles and hour toward the bobble there is a total speen between the two objects of 10 miles and hour therefor it should take less than 2 hours by this calculation you are assuming the bobble is not moving
The variables:
1) you move 7 mph without a current (on a placid lake)
2) the stream's current is 3 mph
3) fisherman releases bobber 14 miles upstream
You begin paddling the moment he releases the bobber. However, you are paddling at 7 mph upstream (against the flow of water which is 3 mph,) therefore you are only making 4 mph headway against the current. The bobber is travelling toward you (from upstream) at 3 mph. It will take you 2 hours, at 4 mph against the current, to travel 8 miles. It will take the bobber 2 hours, at 3 mph flowing with the current toward you, to travel 6 miles.
You and the bobble began this journey at the same moment 14 miles apart. In two hours you traveled 8 miles toward the bobber and the bobble traveled 6 miles toward you. If you add the distance traveled toward each other over that two hour period, you and the bobber traveled toward each other is 14 miles. In two hours. Boink. :)
Finally someone posted the correct solution... If you don't know the answer 100% don't post it. #12's detail is correct, although the solution that the speed of the water moving both the boat and the bobber at the same rate cancels that variable out works, it is merely coincidental, therefore incorrect for a solution. The person who inquired about gravity and water pressure against the boat should maybe switch to another form of problem solving because those questions were not only ridiculous, but completely irrelevant... It was cleared up when told that the boat can travel at 7 mph in placid water (calm/still). Water's consistency does not change when given a motion of 3mph! similarly since we are talking about a STREAM and not a River, i am hoping by "rise rate" of the water you don't mean a tide.... It's a stream! they don't have tides, any other rise and fall of such a small body of water would take to long to play any roll in the equation anyway (whatever roll that may be????)
When it says you can paddle 7 mph on lake placid, shouldn't we assume that that includes all the current condition on lake placid? Otherwise, it should just say that we can paddle our boat 7 mph. If it say we paddle at 7 mph on lake placid and I am on lake placid and I am paddling than I should be moving 7 mph. Therefore, the current should not change my speed calculation only the speed of the bobber.
The bobber moves with the stream, and the boat also, so either way you put it you will add or subtract 3 to each side, but making it easier just eliminate the 3 of the stream, now imagine that the bobber is in a 14m distance from you (its not moving) now you go there moving @ 7mph, therefore: t=d/v t=14/7 t=2.
The answer is 2 hours.
if you're going with the current, then it makes sense that any speed you gain will be cancelled out and you'll arrive in two hours. This isn't explicitly stated one way or the other, but "up stream" to me implies against the current (i.e. salmon swimming upstream to spawn).
Not so much! (#17), I hate to say this but you're an idiot. It isn't "Lake Placid" it's a placid lake, meaning a lake that is placid or without a current. Honestly, think before you post something that makes it sound like an absolute moron.
You can paddle your canoe seven miles per hour through any placid lake. (Meaning that in completely still water, you can go 7 miles per hour)
The stream flows at three miles per hour. (Now assume that you are sitting on a still lake, and the stream flows into it. You are planning to take your canoe up the stream from the lake.)
The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you. (Note, the bobber is not still on the line, because it says he lost it, if it's still on the line, he hasn't lost it.)
How many hours does it take for you and the bobber to meet?
Answer: If you can paddle 7 miles per hour, and the stream is flowing toward you at 3 miles per hour, it is reducing your speed by 3 miles per hour, which means that 7-3=4; you are now traveling 4 miles per hour.
Since the stream is moving at 3 miles per hour, in 1 hour it will carry the bobber 3 miles toward you, while you have moved 4 miles toward it. In 1 hour, both you and the bobber have traveled a combined distance of 7 miles. 4+3=7
The total distance you started with is 14, so, having traveled a combined distance of 7 miles in 1 hour, the amount of time to reach the bobber would be 2 hours. 7x2=14
I have tried to explain this as simply as possible for those who don't understand. I do not believe in making people look stupid because they are 'less intelligent' than myself. However if you don't understand the logic, don't try and argue with it and say that it is flawed. It is not, and you will only make yourself look stupid to those who do understand.
Even a fool, when he keeps silent, is considered wise. ~ Proverbs 17:28
1) you move 7 mph without a current (on a placid lake)
2) the stream's current is 3 mph
3) fisherman releases bobber 14 miles upstream
You begin paddling the moment he releases the bobber. However, you are paddling at 7 mph upstream (against the flow of water which is 3 mph,) therefore you are only making 4 mph headway against the current. The bobber is travelling toward you (from upstream) at 3 mph. It will take you 2 hours, at 4 mph against the current, to travel 8 miles. It will take the bobber 2 hours, at 3 mph flowing with the current toward you, to travel 6 miles.
You and the bobble began this journey at the same moment 14 miles apart. In two hours you traveled 8 miles toward the bobber and the bobble traveled 6 miles toward you. If you add the distance traveled toward each other over that two hour period, you and the bobber traveled toward each other is 14 miles. In two hours. Boink. :)
great puzzle .
The answer is 2 hours.
The stream flows at three miles per hour. (Now assume that you are sitting on a still lake, and the stream flows into it. You are planning to take your canoe up the stream from the lake.)
The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you. (Note, the bobber is not still on the line, because it says he lost it, if it's still on the line, he hasn't lost it.)
How many hours does it take for you and the bobber to meet?
Answer: If you can paddle 7 miles per hour, and the stream is flowing toward you at 3 miles per hour, it is reducing your speed by 3 miles per hour, which means that 7-3=4; you are now traveling 4 miles per hour.
Since the stream is moving at 3 miles per hour, in 1 hour it will carry the bobber 3 miles toward you, while you have moved 4 miles toward it. In 1 hour, both you and the bobber have traveled a combined distance of 7 miles. 4+3=7
The total distance you started with is 14, so, having traveled a combined distance of 7 miles in 1 hour, the amount of time to reach the bobber would be 2 hours. 7x2=14
I have tried to explain this as simply as possible for those who don't understand. I do not believe in making people look stupid because they are 'less intelligent' than myself. However if you don't understand the logic, don't try and argue with it and say that it is flawed. It is not, and you will only make yourself look stupid to those who do understand.
Even a fool, when he keeps silent, is considered wise. ~ Proverbs 17:28