An unmanned aerial vehicle (UAV) carries 45 gallons of fuel. It burns fuel at a rate of 3 gph (gallons/hour) and flies at a speed of 160 mph (miles/hour). We want to fly it to a location X, fly around the area for 1 hour, and then fly it back to the launching point.

Question

How far away can location X be if we want the UAV to arrive back home with a fuel reserve of 0.5 hour?

The greatest number of miles that location x can be is 1120 miles

Answer 1

We will use up 3 gallons flying in a circle for an hour and we want .5*3 = 1.5 gallons left over so we can use
g = 45 - 3 - 1.5 gallons

g gallons * 1 hr/3 gal = x hours to fly out and back

that is x/2 hours one way

so distance = (x/2)*160 miles

Answer 2

g = 40.5 gallons to fly with

40.5/3 = 13.5 hours out and back

so 6.75 hours out

6.75 * 160 = distance out