Helicopter flying around a square course

[giokrutoi]

Homework Statement

helicopter is flying in air it goes A,B,C,D points
which are distributed in square
and helicopter goes one circle in 4 hours
if wind is blowing in direction from A to D
then the whole circle is flown in 3 hours
question: how does it takes to fly from A to C if wind blows in the same direction

Homework Equations

The Attempt at a Solution

if the whole circle needs four hours without wind then to go one section of square needs 1 hour
and let's call the length of one section x and the same will be velocity x km/hour
lets call velocity of wind y
see the graph in the file attached

 

[haruspex]

It is not clear to me whether the flight path is ABCD (not a circuit, or circle) or ABCDA. From the fact that it takes less time with the wind, it seems it must be just ABCD. If so, it takes 4/3 hours per leg without wind.
Also, your diagram is wrong. You have drawn it as though the helicopter still flies as though there is no wind and accepts being blown off course. The only adjustment is to switch to flying back to the West before reaching C. My reading of the question is that the helicopter adjusts so as to still visit all four points.

 

[mfb]

lets call velocity of wind y
see the graph in the file attached

If the helicopter is still supposed to reach B and C, that doesn't work.

helicopter is flying in air it goes A,B,C,D points
which are distributed in square
and helicopter goes one circle in 4 hours
if wind is blowing in direction from A to D
then the whole circle is flown in 3 hours

With wind it is impossible to make the round-trip A->B->C->D->A in less than four hours.

 

[giokrutoi]

If the helicopter is still supposed to reach B and C, that doesn't work.

With wind it is impossible to make the round-trip A->B->C->D->A in less than four hours.

the question is to get to c straight from diagonal
second remark that's why I draw the graph like trapezoid in order to make helicopter fly in 3 hours

 

[giokrutoi]

It is not clear to me whether the flight path is ABCD (not a circuit, or circle) or ABCDA. From the fact that it takes less time with the wind, it seems it must be just ABCD. If so, it takes 4/3 hours per leg without wind.
Also, your diagram is wrong. You have drawn it as though the helicopter still flies as though there is no wind and accepts being blown off course. The only adjustment is to switch to flying back to the West before reaching C. My reading of the question is that the helicopter adjusts so as to still visit all four points.

the only available path is at first from a to b then to c then to d and back to a
and saying it takes 4/3 per leg is wrong four hours is needed to get back to a from a through those other points
on diagram I think that if fling to say from a to b than it will go to point e not to b
and I guess that if It still goes to the same points then it would be impossible to get back in 3 hours

 

[haruspex]

the only available path is at first from a to b then to c then to d and back to a

But why are you so sure it returns to A? Are you sure you are reading the question correctly? I cannot see that allowing it to miss points B and C is an acceptable reading.

 

[mfb]

Even with the shortcut, missing B and C, you cannot make a round-trip in 3 hours. The shortest possible trip will be ~3.7 hours.

 

[giokrutoi]

But why are you so sure it returns to A? Are you sure you are reading the question correctly? I cannot see that allowing it to miss points B and C is an acceptable reading.

can you read Russian ?
if yes text is in file attached here
number 1.3 I translated it the way I understood maybe I am wrong

 

[haruspex]

can you read Russian ?
if yes text is in file attached here
number 1.3 I translated it the way I understood maybe I am wrong

No, I can't read Russian, so I typed it into an online translator and got this:
"The helicopter with there is no wind consistently essential items 1 2 3 and 4 and in the corners of the Square (the shortest distance) for 4h. When the wind, contribute positively in the direction of from 1 to 4, the overflight of the same items for the same route as well..."
(I substituted 1, 2, 3, 4 for A, B, C, D to avoid confusion.)
Sounds to me like it is only saying it visits the four points. Nothing about its being a cycle, or returning to the start. I'll try another translator.

Next translator:
"
Helicopter with absence of wind consistently flies items 1 2 3 and 4 are situated in the corners of a square (the shortest distance) 4h.

When the wind blowing in the direction of from 1 to 4, while overflight of the same items on the same route still..."

 

[mfb]

That still doesn't lead to a solution. If 1->2->3->4 needs 4 hours without wind, with wind it needs at least 3.8 hours.

 

[haruspex]

That still doesn't lead to a solution. If 1->2->3->4 needs 4 hours without wind, with wind it needs at least 3.8 hours.

How true. Maybe the 3h and 4h are swapped around. But I still can't see any implication that the route completes the square.

 

[mfb]

If we swap 3 and 4 hours, then both completing the square and not completing it makes a reasonable problem.

 

[haruspex]

If we swap 3 and 4 hours, then both completing the square and not completing it makes a reasonable problem.

Of course. That's why I mentioned that, even with the times swapped, I don't detect in the translations any implication that the route completes the square.

 

[ehild]

"The helicopter flies over corners of a square A, B, C, and D. Without wind, the route takes 4 hours. If wind blows parallel with the direction from A to D, the same route takes 3 hours. How long does it take to fly along the route AC in the same weather? "According to my dictionary, the word "obletaet" can mean a route A to B, B to C and C to D, but also a route around all points. In this case, the time can not be shorter than 4 hours in wind.
It is not sure if route AC means flying directly from A to C, along the diagonal, or it means ABC?

 

[mfb]

It is not sure if route AC means flying directly from A to C, along the diagonal, or it means ABC?

Probably ABC, but that is a question for later, when the given information is consistent.

@giokrutoi: Please help with the translation issues.

 

[haruspex]

Probably ABC, but that is a question for later, when the given information is consistent.

@giokrutoi: Please help with the translation issues.

For the last part, Google translate gives

How much time will fly by helicopter from AC with the same direction of the wind?

So I would say the question is unclear.
@giokrutoi , if you have the book answer, we might be able to reverse engineer the question. Otherwise I suggest abandoning it as incomprehensible.

 

[giokrutoi]

For the last part, Google translate gives

How much time will fly by helicopter from AC with the same direction of the wind?

So I would say the question is unclear.
@giokrutoi , if you have the book answer, we might be able to reverse engineer the question. Otherwise I suggest abandoning it as incomprehensible.

answer is 1 hour

 

[haruspex]

answer is 1 hour

I tried modelling the following variations:
ABCD (not returning to A) takes 4h no wind, 3h with wind; or swapping 3h and 4h
Wind direction is AD; or wind direction is AC

Results:
4h no wind, 3h with wind, never yields a feasible solution (so no point in trying returning to A)
Otherwise:

ABCD      ABCD         wind           AC with
no wind   with wind    direction      wind
   3          4           AD            0.81
   3          4           AC            0.84
   4         10.2         AD            1
   4         10.2         AC            1
   3          3.0         AD            1
   3          3.1         AC            1

I'm out of ideas.
Note how insensitive it is to whether the wind is AD or AC.
Note also the ambiguity that arises when the ABCD time is the same, with or without wind. Two quite different wind speeds can satisfy the conditions.

 

[mfb]

I don't find a meaningful solution either.