# Joe flies a plane 300 miles in 2 hours to a destination with the wind. On the return trip against the wind, he only flies 270 miles in 2 hours. Assuming wind speed is constant, what's the wind speed?

##### 2 Answers

Airplane = 142.5 mph. Wind = 7.5 mph.

#### Explanation:

Let's think of the problem this way:

**On the first leg of the trip** , Joe flew 300 miles in 2 hours. We can then say that he flew:

Since this was in the same direction of the wind, the plane was going the speed of the plane in still air *plus* the speed of the wind:

**On the return trip**, Joe flew 270 miles in the same 2 hours. We can say that he flew:

Since this was in the opposite direction of the wind, the plane was going the speed of the plane in still air *minus* the speed of the wind:

**Putting it together**

We can add the two equations:

Which means that

The wind speed is then:

Wind speed:

Speed of plane in still air:

#### Explanation:

Flying with the wind Joe flew

Flying against the wind Joe flew

Then we can equate his relative speeds (in still air) there and back to his present location, since the times are the same. We will use

Outbound, Joe's air speed (no wind) is:

The wind has to be subtracted because here it is adding to the speed of the plane in still air.

Inbound, Joe's air speed (no wind) is:

The wind has to be added because here it is reducing the speed of the plane in still air.

Then:

Outbound, Joe's air speed (no wind) is:

Inbound, Joe's air speed (no wind) is: