Respuesta :
Plane's speed without wind i s 117.68 mph
Step-by-step explanation:
We have speed of plane without wind is x.
Distance to brothers place = 200 miles.
A headwind of 20 mph slowed down the plane's speed on the first leg of the trip
Speed to brothers place = x - 20
We have
Distance = Speed x Time
[tex]200=(x-20)\times t_1\\\\t_1=\frac{200}{x-20}[/tex]
A tailwind of 20 mph sped up the plane on the return trip
Speed of return trip = x + 20
We have
Distance = Speed x Time
[tex]200=(x+20)\times t_2\\\\t_2=\frac{200}{x+20}[/tex]
The entire trip took 3.5 hours.
That is
[tex]t_1+t_2=3.5\\\\\frac{200}{x-20}+\frac{200}{x+20}=3.5\\\\200x+4000+2000x-4000=3.5(x-20)(x+20)\\\\400x=3.5x^2-1400\\\\7x^2-800x-2800=0\\\\\texttt{x = 117.68mph or x =-3.40mph}[/tex]
Plane's speed without wind i s 117.68 mph
