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This is the equation for the operations described by the text. Solving for N gives the result.
An equation like this can be simplified significantly, which Katie probably would have done in advance. Then she could solve the simpler equation...
This problem has three variables and two independent equations. This isn't usually enough to solve algebraically, but here they are:
If we can eliminate one of the variables, we might get somewhere with the equations. Toward...
This will require a system of two equations, because there are two variables, airspeed and wind speed. Lets call them A and W, respectively. The first equation will come from the case with the headwind, so A and W are acting in opposite directions.