Northbound buses with tourists leave waco for dallas at 10 minute intervals. the trip takes exactly one hour. southbound tourist buses leave dallas for waco at the same moment as their northbound counterparts and arrive an hour later. how many southbound buses does a northbound bus encounter between waco and dallas, including the one that is arriving in waco just as the northbound bus leaves for dallas and the one that is departing from dallas just as the northbound bus arrives there?

13 buses.

Explanation:

When a Northbound bus leaves Waco there are 7 buses on the way from Dallas, including the one that is arriving at Waco and one departing from Dallas.

If you do not visualize it, think that the Northbound bus departs at 6:00 am, then the bus arriving at Waco departed at 5:00 am, other departed at 5:10am, other at 5:20, other at 5:30, other at 5:40, other at 5:50 and other at 6:00 am. Those are 6 buses that the Northbound bus will encounter on its way.

After that, there will departure other 6 buses that the Nortbound bus will encounter. The times for those departures are: 6:10am, 6:20am, 6:30am; 6:40am, 6:50am and, the last one, 7:00am just when it is arriving.

Therefore, the Northbound bus will encounter 7 buses + 6 buses = 13 buses, which is the answer.