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. The greatest # of miles location x can be is 1120 miles
How far away can location X be if we want the UAV to arrive back home with a fuel reserve of 0.5 hour?
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To find out how far away location X can be, let's break the flight into different segments and calculate the amount of fuel consumed for each segment.
1. Outward Journey: The UAV needs to fly to location X. Since the speed of the UAV is 160 mph and the flight time is 1 hour, the distance it can cover is 160 * 1 = 160 miles. During this journey, the UAV consumes fuel at a rate of 3 gph, so it will use 3 * 1 = 3 gallons of fuel.
2. Flying around location X: After reaching location X, the UAV needs to fly around the area for 1 hour. However, during this time, the UAV will not consume any additional fuel as it will be hovering.
3. Return Journey: After flying around the area, the UAV needs to return to the launching point. The available fuel for the return journey will be the remaining fuel after the outward journey minus the fuel consumed while hovering. The initial fuel was 45 gallons, and the fuel consumed during the outward journey was 3 gallons. Since the UAV burnt fuel at a rate of 3 gph, it consumed 3 * 1 = 3 gallons while hovering around location X. Therefore, the remaining fuel for the return journey is 45 - 3 - 3 = 39 gallons.
Now, let's calculate the distance the UAV can cover on the return journey using the remaining fuel. The fuel consumption rate is still 3 gph, but we need to consider the fuel reserve of 0.5 hours. So the effective flight time for the return journey is 1 - 0.5 = 0.5 hours.
Since the UAV burns fuel at a rate of 3 gph and has 39 gallons of remaining fuel, it can fly for 39 / 3 = 13 hours.
Therefore, the distance the UAV can cover on the return journey is 160 * 0.5 = 80 miles.
Adding the distance covered on the outward journey (160 miles) and the return journey (80 miles), the maximum distance location X can be from the launching point is 160 + 80 = 240 miles.