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

Plane's speed is 150 miles/hour

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 = (Distance)/(Speed)`

So, time on going
`=(720)/((x+30))`

Time on returning
`=(720)/((x-30))`

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

So,
`(720)/((x+30))+(720)/((x-30))=10`

`(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