# The 4200 km trip from new york to san francisco takes 7 h flying against the wind, but only 6 h returning. How do you find the speed of the plane in still air and the wind speed?

##### 1 Answer

#### Answer:

Plane speed

Wind speed

#### Explanation:

To solve these equations we need to manipulate so that we have just 1 unknown and its relationship to some values.

Assumption: the speed (velocity) of the wind is constant

Let the speed of the plane be

Let the speed of the wind be

Let time going be in hours be

Let the time returning in hours be

Note that speed =

So

Consider going: relative to the ground, the actual speed is

Consider returning: relative to the ground the actual speed is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We need this to change things so that, by substitution, we end up with just 1 unknown.

So for going we have:

And for returning we have:

Equation both to each other through distance

Subtract

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using Equation(3) substitute for

Using Equation(4) substitute for