Question

A plane flew 720 mi with a steady 30 mi/h tailwind. The pilot then returned to the starting point, flying against that same wind. If the round trip flight took 10 h, what was the plane's airspeed?
PLEASE HELP ASAP!!

Answer 1

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 .

$Time = \frac{Distance}{Speed}$

So, time on going  $=\frac{720}{(x+30)}$

Time on returning  $=\frac{720}{(x-30)}$

Now we are given that the total time for the whole trip (going + returning) = 10 hours.

So,  $\frac{720}{(x+30)}+\frac{720}{(x-30)}=10$

$\frac{720x-21600+720x+21600}{(x+30)(x-30)}=10$

$720x-21600+720x+21600=10(x+30)(x-30)$

$720x+720x=10(x+30)(x-30)$

$1440x=10(x^2 -[30]^2)$

$144x=x^2 -900$

$x^2-144x -900=0$

$x^2-150x+6x -900=0$

$x(x-150)+6(x -150)=0$

$(x-150)(x+6)=0$

$x= 150,x= -6$

So, the plane's speed is 150 miles/hour