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.
How far away can location X be if we want the UAV to arrive back home with a fuel reserve of 0.5 hour?
whats the second part
well u see SAMAY the answer is in the response, you know, the Thus... part ya soooooooooooooooooooooooooooooo...... Bye now
To find the greatest number of miles away from the UAV's launching point that location X can be, we need to consider the fuel consumption during the round trip.
First, we calculate the fuel consumption for one leg of the trip. The UAV burns fuel at a rate of 3 gallons/hour, and it will be flying for a total of 1 hour to reach location X. Therefore, the fuel consumption for one leg of the trip is 3 gallons/hour * 1 hour = 3 gallons.
Since we want to fly to location X, then fly around the area for 1 hour, and finally fly back to the launching point, we need to account for the fuel consumption during the return leg. So, for the round trip, the UAV will consume a total of 3 gallons + 3 gallons = 6 gallons.
Since the UAV carries 45 gallons of fuel, we can calculate the maximum number of round trips it can make by dividing the fuel capacity by the fuel consumption for one round trip: 45 gallons / 6 gallons = 7.5 round trips.
However, since the UAV cannot make a fraction of a round trip, we need to take the whole number part of 7.5, which is 7. Therefore, the UAV can make 7 round trips.
Next, we calculate the maximum distance the UAV can fly for one round trip by multiplying the speed by the duration of one leg: 160 mph * 1 hour = 160 miles.
Finally, to find the greatest number of miles away from the UAV's launching point that location X can be, we multiply the maximum distance for one round trip by the number of round trips: 160 miles * 7 = 1120 miles.
Therefore, location X can be a maximum of 1120 miles away from the UAV's launching point for the UAV to complete the round trip without running out of fuel.
If we want the UAV to arrive back home with a fuel reserve of 0.5 hours, we need to adjust the number of round trips.
Since the UAV burns fuel at a rate of 3 gallons/hour, it will burn 3 gallons*0.5 hours = 1.5 gallons of fuel during the return leg to account for the fuel reserve.
So, the total fuel consumption for one round trip with a fuel reserve of 0.5 hours is 6 gallons + 1.5 gallons = 7.5 gallons.
Dividing the fuel capacity of 45 gallons by the fuel consumption for one round trip: 45 gallons / 7.5 gallons = 6 round trips.
Multiplying the maximum distance for one round trip by the number of round trips: 160 miles * 6 = 960 miles.
Therefore, if we want the UAV to have a fuel reserve of 0.5 hours, the location X can be a maximum of 960 miles away from the UAV's launching point.