Answer:
The speed of the plane in still air is 89.83 mph and the speed of air is 8.17 mph.
Step-by-step explanation:
Let the speed of the plane in still air is u mph and the speed of the wind is v mph.
Now, the aircraft flew 490 miles in 5 hours with the wind.
Hence, [tex]u + v = \frac{490}{5} = 98[/tex] ........ (1)
Now, the aircraft flew 490 miles in 6 hours against the wind.
So, [tex]u - v = \frac{490}{6} = 81.67[/tex] ............ (2)
Now, adding equations (1) and (2) we get,
2u = 179.67
⇒ u = 89.83 mph
Now, from equation (1) we get,
v = 98 - u = 98 - 89.83 = 8.17 mph.
Therefore, the speed of the plane in still air is 89.83 mph and the speed of air is 8.17 mph. (Answer)
