Question

Problem

At full speed, Hal travels 600 miles in 2 hours
with the wind. The same distance against
the wind takes 3 hours.
What's the maximum speed of Hal's airplane
in still air? What's the speed of the wind?​

Answer 1

The maximum speed of Hal's airplane in still air is:

`v= 250\ miles/h`

The speed of the wind

`c = 50\ miles/h`

Explanation:

Remember that the velocity v equals the distance d between time t.

`v=(d)/(t)` and
`t*v=d`

The distance that Hal travels when traveling with the wind is:

`(2\ hours)(v + c) = 600` miles

Where v is the speed of Hal and c is the wind speed.

The distance when traveling against the wind is:

`(3\ hours)(v-c) = 600` miles

Now we solve the first equation for v

`(2)(v + c) = 600`

`2v + 2c = 600`

`2v= 600-2c`

`v= 300-c`

Now we substitute the value of v in the second equation and solve for c

`3((300-c)-c) = 600`

`3(300-2c) = 600`

`900-6c = 600`

`-6c = 600-900`

`-6c = -300`

`6c = 300`

`c = 50\ miles/h`

Then:

`v= 300-(50)`

`v= 250\ miles/h`

The maximum speed of Hal's airplane in still air is:

`v= 250\ miles/h`

The speed of the wind

`c = 50\ miles/h`