An airplane flies 750 miles due west in 1 1/2 hours and 750 miles due south in 2 hours. What is the average speed of the airplane?
v = (750 + 750) / (2 + 1.5) =
1500 miles / 3.5 hrs = 428.6 miles / hr
To find the average speed of the airplane, we need to calculate the total distance traveled and the total time taken.
1. First, let's calculate the total distance traveled:
Distance traveled due west = 750 miles
Distance traveled due south = 750 miles
Total distance traveled = Distance traveled due west + Distance traveled due south
= 750 miles + 750 miles
= 1500 miles
2. Next, let's calculate the total time taken:
Time taken to fly due west = 1 1/2 hours
Time taken to fly due south = 2 hours
Total time taken = Time taken to fly due west + Time taken to fly due south
= 1 1/2 hours + 2 hours
= 3/2 hours + 2 hours
= (3 + 4)/2 hours
= 7/2 hours
3. Finally, we can calculate the average speed:
Average speed = Total distance traveled / Total time taken
= 1500 miles / (7/2) hours
= 1500 miles * (2/7) hours
= 428.57 miles per hour (rounded to two decimal places)
Therefore, the average speed of the airplane is approximately 428.57 miles per hour.
To find the average speed of the airplane, we need to divide the total distance traveled by the total time taken.
First, let's calculate the total distance traveled:
The airplane flies 750 miles due west in 1 1/2 hours. So, the distance traveled west is 750 miles.
Then, the airplane flies 750 miles due south in 2 hours. So, the distance traveled south is also 750 miles.
Since the two legs of the trip are perpendicular (west and south), we can treat them as the sides of a right triangle where the hypotenuse is the distance traveled. We can use the Pythagorean theorem to find the distance traveled:
Distance = sqrt((distance west)^2 + (distance south)^2)
= sqrt((750)^2 + (750)^2)
= sqrt(562,500 + 562,500)
= sqrt(1,125,000)
≈ 1,060.66 miles
Next, let's calculate the total time taken:
The time taken to travel 750 miles due west is 1 1/2 hours, which is equivalent to 1.5 hours.
The time taken to travel 750 miles due south is 2 hours.
Total time = time west + time south
= 1.5 hours + 2 hours
= 3.5 hours
Finally, we can calculate the average speed of the airplane:
Average speed = total distance / total time
= 1,060.66 miles / 3.5 hours
≈ 303.04 miles per hour
Therefore, the average speed of the airplane is approximately 303.04 miles per hour.