Question

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. What is the greatest number of miles away from the UAV’s launching point can location X be?\

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

all i need is the second part

Answer 1

Flying around for an hour means we waste 3 gal, making our useful fuel only 42 gallons
Only half of that can be used to fly out, or 21 gals
at 3 gal/hr, that makes a maximum flight time of 7 hours
So, at 160mi/hr, that gives a maximum range of 1120 miles

For the reserve fuel, repeat those steps after subtracting 0.5 gal from the available fuel.

Answer 2

3gal/h * (1+ 0.5)h = 4.5 gal reserved.

T = (45-4.5)/3 = 13.5 h = max. driving time to and from X.
1/2 of T is used to drive X miles.
X = r * T/2 = 160 * 13.5/2 = 1080 mi.