A military cargo aircraft flies from Base Alpha to Base Bravo at an average speed of miles per hour. Upon arrival, the aircraft spends exactly hour and minutes on the ground being loaded. It then returns to Base Alpha along the exact same route at an average speed of miles per hour. If the total elapsed time for the entire mission, from the initial departure to the final return, was hours and minutes, what was the aircraft's overall average speed, in miles per hour, for the entire mission?
Answer: 320 mph
Answer
The aircraft's overall average speed for the entire mission was miles per hour.
The correct overall average speed is found by first calculating the total distance traveled, and then dividing it by the total elapsed time for the mission. By subtracting the -hour ground delay from the -hour total time, we find the aircraft flew for a total of hours. Using the relationship , we find the one-way distance is miles. Therefore, the total round-trip distance is miles. Dividing the miles by the total mission time of hours yields an overall average speed of mph.
Step-by-Step Solution
Key Concept
Overall average speed is the total distance traveled divided by the total elapsed time, which includes any stationary delays. It cannot be calculated by simply averaging the individual speeds.
Alternative Method
Instead of solving for distance first, you can use the harmonic mean of the speeds to find the average speed while in the air: . The aircraft flew for hours at an average of , covering miles. Then, divide miles by the total mission time ( hours) to find the overall average speed: .
Estimated Time:3m 0s