> User Inputs their Postcode
> This gets sent, with my postcode, to the API
> The API returns, amongst other things, a calculated Travel Time
> This Travel Time gets multiplied by my Hourly Rate
> The total Travel Cost is presented to the user.

You can't do it using Google's Directions service, the terms of use
require you to display the results (map or text) of any directions
query.

If you are not requiring taxi-fare levels of accuracy, you could make
an approximation based on calculated straight line distance.  You'd
need to geocode the postcodes, but may not use Google's services for
that as you are required to display the results again ... but there
are other geocoders
http://groups.google.com/group/google-maps-api/web/resources-non-google-geocoders

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