Question

Jeff earned his pilot's license and flew to visit his brother 200 miles away. A headwind of 20 mph slowed down the plane's speed on the first leg of the trip, while a tailwind of 20 mph sped up the plane on the return trip. The entire trip took 3.5 hours. Choose the equation that will find x, the plane's speed without wind.

Answer 1

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

         $200=(x-20)\times t_1\\\\t_1=\frac{200}{x-20}$

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

         $200=(x+20)\times t_2\\\\t_2=\frac{200}{x+20}$

The entire trip took 3.5 hours.

That is

            $t_1+t_2=3.5\\\\\frac{200}{x-20}+\frac{200}{x+20}=3.5\\\\200x+4000+2000x-4000=3.5(x-20)(x+20)\\\\400x=3.5x^2-1400\\\\7x^2-800x-2800=0\\\\\texttt{x = 117.68mph or x =-3.40mph}$

Plane's speed without wind i s 117.68 mph