An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 5 hours and 30 minutes. The return flight took 5hours. If the distance from Joppetown to Jawsburgh is 1600

​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.

To find the airspeed of the plane and the speed of the wind, we'll need to set up a system of equations using the information given.

Let's denote the airspeed of the plane as "p" and the speed of the wind as "w".

We know that the time it took for the plane to fly from Joppetown to Jawsburgh (with a headwind) was 5 hours and 30 minutes. Given that the distance is 1600 miles, we can use the formula distance = speed × time to set up the equation:

1600 = (p - w) × (5.5)

Similarly, for the return flight (with a tailwind), the time taken was 5 hours. Using the same formula, we get:

1600 = (p + w) × (5)

We now have a system of two equations. Let's solve it using a method called substitution:

From the first equation, we can isolate p - w by dividing both sides by 5.5:

1600 / 5.5 = p - w
291.58 = p - w

Now we substitute this value of p - w into the second equation:

1600 = (p + w) × 5
1600 = (291.58 + w + w) × 5
1600 = (291.58 + 2w) × 5
1600 = 1457.9 + 10w
142.1 = 10w
14.21 = w

We have found the value of w, the speed of the wind. Now we can substitute this value back into either of the original equations to find the airspeed of the plane:

1600 = (p - 14.21) × 5.5
1600 = 5.5p - 5.5 × 14.21
1600 = 5.5p - 78.155
1678.155 = 5.5p
p = 305.2109

So, the airspeed of the plane is approximately 305.21 mph and the speed of the wind is approximately 14.21 mph.

To summarize:
- Airspeed of the plane (p) = 305.21 mph
- Speed of the wind (w) = 14.21 mph

Vp*t = 1600.

Vp*5 = 1600, Vp = 320 mi/h. in still air.

(Vp-Vw)*5.5 = 1600.
5.5Vp - 5.5Vw = 1600.
5.5*320 - 5.5Vw = 1600, Vw = ?.