Respuesta :
Answer: the speed of the wind is 40 mph
Step-by-step explanation:
Let x represent the speed of the wind.
A jet aircraft can average 160 miles per hour in calm air. On a trip, the aircraft traveled 600 miles with a tailwind. This means that the total speed of the jet aircraft is 160 + x mph
Time = distance/speed
Time taken to cover 600 miles would be
600/(160 + x) - - - - - - - - 1
It returned the 600 miles against a headwind of the same speed. This means that the total speed of the jet aircraft is 160 - x mph
Time taken to return would be
600/(160 - x)
If the total round trip took 8 hours, it means that
600/(160 + x) + 600/(160 - x) = 8
Multiplying through by (160 +x)(160 - x), it becomes
600(160 - x) + 600(160 + x) = 8(160 +x)(160 - x)
96000 - 600x + 96000 + 600x = 8(25600- 160x + 160x - x²)
192000 = 8(25600 - x²)
204800 - 8x² = 192000
204800 - 192000 = 8x²
8x² = 12800
x² =12800/8 = 1600
x = √1600 = ±40
x = 40 mph
