# Wolfram Mathematica

## Travel Time & Distance

Estimate distance and duration of a road trip.

Travel between two distant cities.

In[1]:=
```cities = {Entity["City", {"Lisbon", "Lisboa", "Portugal"}], Entity["City", {"Beijing", "Beijing", "China"}]};```

This is the geodesic distance between them.

In[2]:=
`GeoDistance[cities]`
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This is the length of the computed road trip.

In[3]:=
`TravelDistance[cities]`
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And this is the estimated driving time, assuming continuous driving with no stops.

In[4]:=
`TravelTime[cities]`
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This object contains the actual set of travel instructions.

In[5]:=
```td = TravelDirections[{Entity[ "City", {"Lisbon", "Lisboa", "Portugal"}], Entity["City", {"Beijing", "Beijing", "China"}]}]```
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Represent the trajectory (in red) on a Mercator map and compare with the geodesic trajectory (in blue), which is shorter, as you saw before.

In[6]:=
```GeoGraphics[{Thick, Red, GeoPath[td], Blue, GeoPath[{Entity["City", {"Lisbon", "Lisboa", "Portugal"}], Entity["City", {"Beijing", "Beijing", "China"}]}]}, GeoProjection -> "Mercator", GeoGridLines -> Automatic]```
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An azimuthal projection shows more clearly that the geodesic is shorter than the travel path.

In[7]:=
```GeoGraphics[{Thick, Red, GeoPath[td], Blue, GeoPath[{Entity["City", {"Lisbon", "Lisboa", "Portugal"}], Entity["City", {"Beijing", "Beijing", "China"}]}]}, GeoProjection -> "Mercator", GeoGridLines -> Automatic]; Show[%, GeoProjection -> "LambertAzimuthal", GeoZoomLevel -> 4]```
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