2 doctors agreed: No: I know of no research that shows xenical can cause a false-positive drug test. All xenical does is block some of the fat from your diet from being absorbed, thus decreasing your calorie intake. This shouldn't cause either a urine or a blood drug test to become positive.
The total flight duration from New York, NY to Dominican Republic is 3 hours, 31 minutes. This assumes an average flight speed for a commercial airliner of 500 mph, which is equivalent to 805 km/h or 434 knots. It also adds an extra 30 minutes for take-off and landing.
Non-stop flight time from Manchester, NH to Washington, DC is around 2 hours. Fastest one-stop flight between Manchester, NH and Washington, DC takes close to 4 hours. However, some airlines could take as long as 18 hours based on the stopover destination and waiting duration. This is the average non-stop flight time from Manchester, NH to either of the major airports that serves Washington, DC.