Answer: the device flies at 27 mph in still air
Explanation:
Let x represent the speed of the home coming device in still air.
On takeoff, the device encountered a tailwind of 9 mph and made the delivery in 15 minutes(15/60 = 0.25 hours). It is assumed that it travelled in the direction of the wind. This mean that the total speed would be
(x + 9) mph
Distance travelled = speed × time
Therefore, distance covered during delivery would be
0.25(x + 9)
The return trip into the wind took 30 minutes(30/60 = 0.5 hours). This means that it travelled against the wind direction. The total speed would be (x - 9) mph.
Distance travelled on returning would be
0.5(x - 9)
Since the distance travelled is the same, then
0.25(x + 9) = 0.5(x - 9)
0.25x + 2.25 = 0.5x - 4.5
0.5x - 0.25x = 2.25 + 4.5
0.25x = 6.75
x = 6.75/0.25
x = 27 mph