math problem distance of x
Hi,
To find the distance X what do i do?
This is not homework BTW.
I travel from Pt A to the the other side at 5km/hr, then I head north at 3km/hr.The side lengths are given.
I can use Pythag theorum to find side length of the right angle triangle of distance traveled.
To find the distance X what do i do?
This is not homework BTW.
I travel from Pt A to the the other side at 5km/hr, then I head north at 3km/hr.The side lengths are given.
I can use Pythag theorum to find side length of the right angle triangle of distance traveled.
ASKER
the angles are unknown apart from 90
You need either the angles or the time you travel either the overall distance or of one of the legs or the overall distance.
The angle at which you start your journey will suffice. What is it? You say you don't know. Hence it seems an unsolvable problem.
can you post the entire question - perhaps there is some missing information!
Given that you are given rates, you are possibly missing the total time of travel, T.
h^2 = 2^2 + x^2
T = t_h + t_north
t_h = h/5
t_north = (5-x)/3
T = h/5 + (5-x)/3
5T = h + 5(5-x)/3
h = 5T - 5(5-x)/3
2^2 + x^2 = 25 [ T - (5-x)/3 ]^2
Solve for x..
h^2 = 2^2 + x^2
T = t_h + t_north
t_h = h/5
t_north = (5-x)/3
T = h/5 + (5-x)/3
5T = h + 5(5-x)/3
h = 5T - 5(5-x)/3
2^2 + x^2 = 25 [ T - (5-x)/3 ]^2
Solve for x..
Maybe the idea is to minimize the total time of travel?
hmm, then the x would not make sense. As the minimum total time would with no second leg with 3km/h.
Or, maybe the problem is to maximize the total time of travel?
Both questions make sense if there is an answer.
But at this point, I will stop guessing as to what the question is and let the author tell us. The author got the problem from somewhere, and if not transmitted verbally, we should be able to get the true question.
Both questions make sense if there is an answer.
But at this point, I will stop guessing as to what the question is and let the author tell us. The author got the problem from somewhere, and if not transmitted verbally, we should be able to get the true question.
But still it can be fun to play with the question
The max time will be 2.1 hour
the min time would be 1.07 hour
and the plot of t(x) was more complicated than I wanted to spend the time on.
The max time will be 2.1 hour
the min time would be 1.07 hour
and the plot of t(x) was more complicated than I wanted to spend the time on.
A more interesting question might swap the two speeds.
ASKER
Hi Sorry I dont have more information as it it to solve the distance x.
The speeds are given for the directions 3km/hr and 5km/hr.
is this problem unsolvable?
The speeds are given for the directions 3km/hr and 5km/hr.
is this problem unsolvable?
If you want to minimize the total travel time, and if the speeds are swapped, so that it is 3km/hr for the part from A to the other side, and 5km/hr for the part from x to B, then you can solve it by taking the derivative of the total travel time, or, a little geometry should show that you want the ratio of the speeds to be the same as the ratio between the length of x and length of the segment from A to x
>is this problem unsolvable?
I agree that problem is unsolvable with the given information!
I agree that problem is unsolvable with the given information!
The stated problem is "To find the distance X what do i do?"
The answer to that problem is: Determine what conditions you want X to satisfy.
If you want to find X that minimizes the total time of travel, and if the speeds are stated correctly, then the total time of travel is minimized when X = 5k.
If you want to find X that minimizes the total time of travel, and if the stated speeds are swapped, then the total time of travel is minimized when X = 1.5k.
The answer to that problem is: Determine what conditions you want X to satisfy.
If you want to find X that minimizes the total time of travel, and if the speeds are stated correctly, then the total time of travel is minimized when X = 5k.
If you want to find X that minimizes the total time of travel, and if the stated speeds are swapped, then the total time of travel is minimized when X = 1.5k.
>To find the distance X what do i do?, THAT is the question, not "To be or not to be?"
If you stand still, you are not away from anywhere. :-)
>> Hi Sorry I dont have more information as it it to solve the distance x.
>> The speeds are given for the directions 3km/hr and 5km/hr.
As you gather by now, the question is not stated in a way to give a solution. We have suggested a number of potential questions; and we can probably come up with dozens more.
Let's try to put this question in some context. Where did you get the numbers that you stated? Why are you trying to solve this question? Who gave the question to you? If you get the answer after first figuring out what the question is, what will that affect?
Maybe from your reply, we can discern what the intent of this question is. If not, then probably deleting this question is the best option.
>> The speeds are given for the directions 3km/hr and 5km/hr.
As you gather by now, the question is not stated in a way to give a solution. We have suggested a number of potential questions; and we can probably come up with dozens more.
Let's try to put this question in some context. Where did you get the numbers that you stated? Why are you trying to solve this question? Who gave the question to you? If you get the answer after first figuring out what the question is, what will that affect?
Maybe from your reply, we can discern what the intent of this question is. If not, then probably deleting this question is the best option.
ASKER
The question came from a secondary student who wanted me to explain this, I couldnt do it so I posted it here.
How long does it take to travel the route so x is covered is the question.
How long does it take to travel the route so x is covered is the question.
ASKER CERTIFIED SOLUTION
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Ozo's comment (ID: 40135874) should be taken seriously.
I would have thought that, if one swaped the times, the first leg would be by boat across the river, the second then by walking.
I would have thought that, if one swaped the times, the first leg would be by boat across the river, the second then by walking.
ASKER
ok thanks I will look at the soln provided
"both legs require the same time" and "both legs the same length" are among the conditions one may decide to impose in order to choose a particular X, although they strike me as less interesting, less useful, and less likely to be posed in a puzzle than minimizing total travel time.
This is a simple minimum search (curve sketching)..
At what angle (0 > theta < 90)?