Answer:
Plane's speed is 150 miles/hour
Step-by-step explanation:
Let the plane's airspeed be x
Speed of wind is 30 miles/hour
When a plane flew with the wind , Speed = (x+30)
So, the speed plain with wind on going = (x+30)
Since we are given that on returning plane fly against the wind .
So,When a plane flew against the wind , Speed = (x-30)
So, the speed plain against wind on returning = (x-30)
Distance = 720 miles .
[tex]Time = \frac{Distance}{Speed}[/tex]
So, time on going [tex]=\frac{720}{(x+30)}[/tex]
Time on returning [tex]=\frac{720}{(x-30)}[/tex]
Now we are given that the total time for the whole trip (going + returning) = 10 hours.
So, [tex]\frac{720}{(x+30)}+\frac{720}{(x-30)}=10[/tex]
[tex]\frac{720x-21600+720x+21600}{(x+30)(x-30)}=10[/tex]
[tex]720x-21600+720x+21600=10(x+30)(x-30)[/tex]
[tex]720x+720x=10(x+30)(x-30)[/tex]
[tex]1440x=10(x^2 -[30]^2)[/tex]
[tex]144x=x^2 -900[/tex]
[tex]x^2-144x -900=0[/tex]
[tex]x^2-150x+6x -900=0[/tex]
[tex]x(x-150)+6(x -150)=0[/tex]
[tex](x-150)(x+6)=0[/tex]
[tex]x= 150,x= -6[/tex]
So, the plane's speed is 150 miles/hour
