posted by School123 .
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?
after t hours, you have gone 160t miles
and you have burned 3t gallons of fuel
So, you are burning fuel at the rate of 160/3 miles/gal
You have 45 gallons of fuel, but you wast 3 gals flying about, so you have a range of
160/3 * 42 = 2240 miles
Thus, you can't go more than 1120 miles away and make it back.