Question 1189898
<font color=black size=3>
p = speed of the plane in still air (i.e. without any wind).
w = speed of the wind
speeds are in km per hour


Here are some useful terms to keep in mind<ul><li>headwind = the wind that pushes against the head of the plane to slow it down. The wind is moving the opposite direction as the plane.</li><li>tailwind = wind that pushes against the tail to speed the plane up. The wind is moving the same direction as the plane.</li></ul>In short,<ul><li>headwind = slows plane down</li><li>tailwind = speeds plane up</li></ul>Headwind:
When traveling against the wind, the headwind has the original plane speed (p) drop to p-w
distance = rate*time
distance = (p-w km/hr)*(9 hours)
distance = (p-w)*(9)
distance = 9(p-w)
We're told that the plane is able to travel 6282 km when encountering the headwind
So the first equation we can set up is
9(p-w) = 6282


Let's solve for p
9(p-w) = 6282
9(p-w)/9 = 6282/9
p-w = 698
p-w+w = 698+w
p = 698+w


Tailwind:
When traveling with the wind, the tailwind has the original plane speed (p) bump up to p+w
Through similar calculations as the headwind, we'll have...
distance = rate*time
7992 = (p+w)*9


From here, plug in p = 698+w and isolate w.
7992 = (p+w)*9
7992 = (698+w+w)*9
7992 = (698+2w)*9
7992 = 6282+18w
7992-6282 = 18w
1710 = 18w
18w = 1710
w = 1710/18
w = 95
The wind speed is 95 km per hour 


Use that value of w to find p
p = 698+w
p = 698+95
p = 793
The plane travels at a speed of 793 km/hr if there wasn't any wind at all.


---------------------------------------------


Answers: 
Plane speed in still air = <font color=red>793 km per hour</font>
wind speed = <font color=red>95 km per hour</font>

</font>