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
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.
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.
To determine the farthest location X can be if we want the UAV to arrive back home with a fuel reserve of 0.5 hours, we need to calculate the total distance the UAV can travel within the given fuel capacity and time constraints.
Let's break down the steps to get the answer:
1. Calculate the total fuel consumed on the round trip:
- The UAV burns fuel at a rate of 3 gallons per hour (gph).
- The round trip consists of flying to location X, spending 1 hour there, and returning to the launching point.
- So, the total time for the round trip is 1 hour (to location X) + 1 hour (flying around) + 1 hour (returning to the launching point) = 3 hours.
- The total fuel consumed is 3 hours * 3 gph = 9 gallons (3 gph * 3 hours = 9 gallons).
2. Calculate the maximum distance the UAV can fly with the remaining fuel:
- The UAV carries 45 gallons of fuel in total.
- Therefore, with 9 gallons already consumed, there are 45 gallons - 9 gallons = 36 gallons of fuel remaining.
- To find the maximum distance that can be covered with this fuel reserve, we need to know the UAV's fuel efficiency in terms of miles per gallon (mpg).
- Suppose the UAV's fuel efficiency is described as 10 miles per gallon (mpg).
- The maximum distance that can be covered with 36 gallons of fuel is 36 gallons * 10 mpg = 360 miles (36 gallons * 10 mpg = 360 miles).
So, if we want the UAV to arrive back home with a fuel reserve of 0.5 hours, the greatest number of miles away from the launching point that location X can be is 360 miles.