I'm trying again because it seems as if I was too vague in my previous question.
The exact information I was given to solve the problem:
A hot air balloon travels from the point O to the target point M. The wind speed varies at different altitudes, which means that the pilot can control the horizontal movement by altering the height of the balloon. On the day of the flight, the horizontal wind speeds at 2 different altitudes are given:
y1 = 0.9
The 2 wind speeds are illustrated with dotted lines on pic 2. The wind speeds are measured in meter/second.
There are 2 real numbers: s and t in the case of pic 3
Earlier in the assignment, I was informed about the values of pic4, pic5, pic6
The vector: pic4 consists of 2 points, O and M. O = (0;0) and M = (3000;1000). I calculated the length of pic4 to be 3162.277m.
The vector: pic5 consists of 2 points, (4;0.9). I calculated the length of pic5 to be 4,1m.
The vector: pic6 consists of 2 points, (4;3). I calculated the length of pic6 to be 5m.
I also found the angle between the 2 vectors (V1 and V2) which is 49.556.
With this information I put the values into the formula and got the following equation:
3162.277=s*4.1+t*5
What I don't understand is how to find the values of s and t, because when I try to solve for either, I always end up with a new equation instead of a number.
No. This is certainly not what you want to solve for. I suppose the problem statements asks for the time $s$ to be spent at the first altitude and the time $t$ to be spent at the second altitude in order to arrive at point $M$ from point $O$. Your calculation results in (various possible choices of) such times in order for the zigzag distance travelled to be the same as the distance from $O$ to $M$.
Rather, if the twi simes are $s$ and $t$, observe that you travel a total of $4s+4t$ to the east and $y_1s+4t$ to the north. Equate these expressions with the desired $3000$ east and $1000$ north distances and then solve this system of two linear equations in two unknowns for $s$ and $t$. Actually, this is precisely whet $\vec{OM}=s\vec{v_1}+t\vec{v_2}$ expresses.