Respuesta :
Answer: the speed of the plane in still air is 101.2 mph
Step-by-step explanation:
Let x represent the speed of the plane in still air.
The pilot flew his single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.
Time = distance/speed
Time spent while going is
60/(x + 30)
He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.
Time spent while returning is
60/(x - 30)
If the total time going and returning was 1.31.3 hours, it means that
60/(x + 30) + 60/(x - 30) = 1.3
Cross multiplying, it becomes
60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)
60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)
120x = 1.3x² - 1170
1.3x² - 120x - 1170 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1.3
b = - 120
c = - 1170
Therefore,
x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3
x = [120 ± √(14400 + 6080)]/2.6
x = [120 ± √20480]/2.6
x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6
x = 101.2 or x = - 8.9
Since the speed cannot be negative, then x = 101.2 mph
